T  F 


UC-NRLF 


SB    31b 


LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


RAILROAD    CURVE 
TABLES 


CONTAINING 

A  COMPREHENSIVE  TABLE  OF  FUNCTIONS 
OF  A  ONE-DEGREE  CURVE,  WITH  COR- 
RECTION QUANTITIES  GIVING 
EXACT  VALUES  FOR  ANY 
DEGREE  OF  CURVE 

TOGETHER    WITH 

VARIOUS    OTHER   TABLES    AND    FORMULAS,  INCLUDING 
RADII,  NATURAL  SINES,  COSINES, 
TANGENTS,   COTANGENTS,  ETC. 

TO    WHICH    IS    ADDED 

A  METHOD  OF  FINDING  ANY  FUNCTION  OF  A  CURVE 
OF     ANY     DEGREE    OR    RADIUS 
WITHOUT     A     FIELD      BOOK 


By 
R.   S.   HENDERSON 


OF   THE 

UNIVERSITY 

OF 


NEW  YORK 

THE  ENGINEERING  NEWS  PUBLISHING  Co. 

1906 


eENEHAL 


COPYRIGHT,    1906, 
BY 

R.  s.  HP:NDERSON. 


J.   F.    TAPLEY  CO., 

BOOK    MANUFACTURERS, 

NEW    YORK. 


PREFACE. 


This  little  volume  is  intended  to  supplement  existing 
field  books.  Consequently  the  usual  theoretical  discussions 
have  been  omitted  and  the  book  reduced  in  size  as  much  as 
possible.  It  is  believed,  however,  that  these  tables  will 
prove  amply  sufficient  to  meet  the  demands  of  the  field 
engineer. 

The  correction  quantities  are  original  in  that  they  are 
applicable  to  any  function  of  a  curve  and  are  independent 
of  the  central  angle.  The  rectangular  co-ordinates,  X  and 
Y,  are  believed  to  be  entirely  new.  The  appendix,  "Field 
Engineering  Without  a  Field  Book,"  is  here  presented  for 
the  first  time. 

The  computations  have  been  made  with  extreme  care. 
The  approximation  of  5,730  feet  for  the  radius  of  a  one- 
degree  curve,  used  in  several  previous  books,  has  not  been 
permitted  in  the  preparation  of  the  present  volume. 

While  every  effort  has  been  made  "to  secure  absolute 
accuracy  in  the  tables,  the  author  makes  no  claim  to  infalli- 
bility. Should  any  errors  be  discovered,  however  slight,  a 
favor  will  be  conferred  by  reporting -the  same  to  the  pub- 
lishers. 

Chicago,  July,  1906.  R.  S.  HENDERSON. 


204109 


CONTENTS. 


PAGE. 

Explanation  of  Terms 1 

Use  of  Tables 2 

Table  I.     Minutes  in  Decimals  of  a  Degree  and  Length 

of  a  1°  Curve 9 

Table  II.     Functions  of  a  1°  Curve 10 

Table  III.     Correction  Quantities 52 

Table  IV.     Curves  Designated  by  Radius 55 

Table   V.      Radii 56 

Table  VI.    Natural  Sines  and  Cosines .-  58 

Table  VII.     Natural  Tangents  and  Cotangents GO 

Table  VIII.     Frogs  and  Switches 61 

Table  IX.    Standard  Rail  Sections 61 

Table  X.    Inches  in  Decimals  of  a  Foot 61 

Table  XL    Trigonometrical  Formulas 62 

Trigonometrical    Formulas 62 

Miscellaneous  Formulas  and  Their  Application 63 

Appendix.    Field  Engineering  Without  a  Field  Book.  .  .  66 


TABLES 


EXPLANAT/ON     OF     TERMS. 


FORMULAS     FOR    A    I     CURVE. 

f&dios  *  R 


T  = 


Eternal  Secant  -  E  =  F?  exsec^  A 


Middle  Ordinote  =  M= 
Recton^ular  Co-ordinate   X  =  Rsin  A 
Rectangular  Co-ordinate    Y=  F?vers  A 
Length  of  Curve  =  l_  =  100  A 


RAILROAD   CURVE  TABLES 


/.  To  f.orf 

For  a    J°  curve.. 

T-25Z6.I  Cor  -  0.19 

E  =  S3Z.14-  Cor.  =  0.04 

C  =  46221.8  Cor.  =  0.34 

M  =  4-S6.9/  Cor.  =  0.04 

X  =  4-Z30.0  Cor.=  0.3/ 


U5E    OP   TABLES. 
functions    of  a   <5°  curve    if  A  -4-7-35. 

(Tables  I,  II  anJ  HI.) 

For  o  6°  curve . 


E  = 
C~ 


=  4ti.2\ 
+  0.04=  o8.73 


-  81.19 


+ 0.14- =3/0.% 


L  =47X100+5833=  4/S8.33 


2.   To   f/W  T^e   functions     of  o  curve    of  22o'  radius    if 
(Table*  I,  II  and    IV.) 


For  o    /*    curve. 
r=S973.l 

E- 2547. 2 

C  =8269.7 
M  =  /7^3.3 
No    correcti'on     required.       Degree    of   curve  -26°-t6A 

J5Y.62 


For  o  curve  of  22o   rcruxjs . 

T  -5973.1  X  .038397  -  229.35 
E  =  ^54 7.  a  X  .038397  =  97  9O 
C  =  82£9.7  X  .038397=  ^17.^3 
.038397=  67.71 


/f    chaining    begins    at    C/?G   en<J    Of  curve.    1he   sub-chord 
at   ihe    otier    eW  w/'/f   te     5"/.62^  ^?j  *.04%=  51.62 +0.33=  51.95, 
J-  -  35-/-9S    ^stead     of     35X-62 


RAILROAD  CURVE  TABLES 


J.    £Txa/rro/e     showing    o&D//cation     of   the    /"  curve   fi//7C^Vor>s    in    poss 
ing     obstacles-  (Tables   I,  II  an</ Jii^' 

Gt've/7     two   tangents    t0fersect/jfg    oppos/fe  &   &/?</  24-7'  from  Q 
building.          &-F9°-43.        5tat'b/7   of    PI-   =48+1  i.6 

Required    to    run   in    The    flattest    curve   of   even    degree    or 
half   degree    that   will  c\ear  the    kvilding    bu    not   less    thffff  So'. 

Maxi'murr?    allowable,    value   of  £"="  Z47-SO  =*/97.' 

For  A  =59-4,5'     T,  =  -32S9.Z,      E,=  9/^.97     and  L,  -S97/.7 


~|2r  =  4.4-5-        Ke/?ce    use  4°-3o'  curve.       ^—  =  194.9  =  E+.,0  . 


Station    of  P.I. 

T  =     7+31.1 
Station    of  P.C.  =  4-0+90.5" 
L    ~   13+27.0 
Station  of  P.T.=  54  +  07.5" 
Sub -chord    from  PC.  to' Station  41  = /9.f 
Def /eat/on   in  minutes  =  3D*  sub-chord  =.3X4.5X/9.5 
=  £6.  Hence    deflections   from   P.C.   are  as 

fol/ows:       41,   O°-26'.     42,  2°-4l'.     43,  4°'S6'.         44, 
7-//.'     4S,    3°-Z6'.     46,    H'~4l'.     4-7,  /3°-5~(>', 

W/^  transit  at  P.I.  (after  A  has  been  /Treasured) 
set  P.C.  at  station  4O+8O.5  and  sef  P.T.  on  for- 
ward tangent  73/-/'  from  PI. 

W,'fJi    transit  at  PC.  set  stations   41  and  AZ    by 
chi lection s .  O/?  accou/jf  of  obstacles    on  l/fle. 

stations   43,  44,  45  and  46    are     invisible     from 
P.C .        Central  angle  to  station  4-3  =  2 y(4°-5(>')  -  9- 5?'. 


RAILROAD   CURVE  TABLES 


For  &  =  9°S2'       X,  -  981.  81 

y,=  54.75 

d-alting    PC.  station   0    set  Q  pcxnt  A     of     2-A/8.2     on    svbtongznt. 
Set    station   4-3    by    measuring     18.23'  irom   A    ond    foo'    frc/r?    slo 
t/on  42. 

Centra/   angle  to   station   4*4  =  (9°-S2')+(4*-Jo)  *  /4°-22 


For  4  =  I4'-Z2       X,  =  14-21.7  =    3/5.3 


~~ 


5e/  Q  poinf  B  at    slaf/c/r    J//5T9    on    subtangent.         5e/ 
44-    by      measuring    39.92     fro/7?  B     and^     /oo'    from     slat/on 
imilarl      for  station  45,    A  -  /8-52\     X.^/SSz.?,     X4.,0= 


4//.T 
t  =30783  j      \,0~  68.41        5et  o   po'/ot  f  of   station  4+//.7    o 

For  stat.'on    47,  A  =  27-S2'          C,  -  27533  ^"f^  ~  6/3-  ;  8  Cor-  =  °-^ 

6/3.18  +  O.tS  -  6/3.  33  =  C4.,0  ,  Set     station    47    by     chord    distance. 

6/J.53'  //v/?   /?C.  £?/7<y    deflection    /3°-56'. 

Otstoc/es     oo    hi?e     prevent     setti/ia     station   45     t>w     measunna    jroiT) 
station   4-4  or  46.  W/'/fr     "transit   at   F    se~f   station    45  by  meos- 

ur/nQ     (?$.4-l'   of     r/qht     a/r<j/es     to     sub-ta/>(j€>nf  . 

W/"M     transit   at     station    4~7   jef    static/75    4-6  and  48    by  Jet/ec- 
t~i<y/7S  .  On    account"   of    ob$tac/es    on    ///?e     stations     ^9    and  SO   ore 

inv/5/6/e     from    stah'on  47.  Central  angle    station  47  fo  51  ~  /8'-O'. 


/#°-o'     C,-  1792.6  =  398.  36          Cor.*0./O 

7t>  F4 

C4.}0.  AT,  =  70.  f  4          -££-  =  /ff.68  -  /K-,o 

Set  station  SI    bu   chore/   398.  4(>'   from    sfat~icii  4-7    and  ^er/ec//o/7 
5-  O     fro/77    f0/?<fes>t~  at    sla'ton   4  7. 

Set  a  po/r?f   H    on    the    cJrord    IOO'  Jrctn    static*  47  and  measure. 
c//s/bflce     fro/77  )-/    fo     staf/on    4-8.  Set    o  po//jt    tf  on   J/>e 

chore/    IOO'  from   stot/ofi  SI.         Set   static/?  SO   6 


RAILROAD   CURVE  TABLES 


from  station  SI  aa</  the  some  </tsfa/?ce  front  K  Q5  H  /?  from  stq- 
1/ofl  4g.  5et  o  point  G  at  center  of  chord.  Set  station  49  by 
measuring  /S.68  from  O  and  /oo'  frvm  star  hot?  SO. 

YV/M     transit   at    P.  T.     set  stafws    S2,  S3  a*</  f4    by    deflect/ens 
and  check    on     statin  S/. 

In    He    foreyotne)     examp/e    f^e     corrections     are    used     onk  w^ere 
necessary.       A     little,   practice    w///   indicate,    where    they    shou/</    te 
usec/     and    where  1ne»j    may    be.    om;fte</. 

4.   Use  of    co -ore/mates    X   and  Y    as    applied  1b    reversed   curves. 
Given    two   tangents    rnafd'n^   on    angle    of    JO-f*'  w//^    each  otter* 
/?eay/rec/    to    connect  them    w»//7   an   d°  re.ve.rsed  cur^e.       The.  curve 
is    to    Jecwe   the    first  tangent  ot  a  point  H,     the  perpendicular 
distance.    Hf~  being   9735' 


If  "H>e  curve  HZ  »'s  proc/uce</  beyond  H  1b  B  //jcreas/0<f  $ 
centra/  a^/e  INJ  /O-/4'  ^e  tangent  fe  the.  curve  of  5  will  be. 
parallel  ~k  tire,  second  tangent  F~N. 


For 


X,  = 


'09.74 


S4.37X9  =434.96         Cor  =.04*8 
4  34.96 -.32  =  434.64  =X  for  centra/    angle  a.       Hewce    as 


RAILROAD   CURVE  TABLES 


For    A  = 


92  =VN~0 

of  cur*? 

of  curve 


5".      Use    of   /77/</c//e    orc/i'nates     /o 
ny  /e. 


=  273  70         Cor    ~   OS?  £73.701 

I44>  58  -QK  -TV. 


o    cury^  o 


tral 


Bisect  chore/  0G  o/  A/ 
Connect  H  an^   F. 


243.3 


Draw   P2    perpendicular   to    chor</   KG 
'nf-   P,          Draw  Q5    perpendi<z\>\ar    /b  cliord 
fff/'t/d/e    point"  Q. 


T/ros    t«j    swcce55/^e  ' 
plotted     or?    tie    curve. 


<7/?y    numher    of   points     may  be 


6.     Use    of   X,  Y  aaj  C    in     plott,ng    a    curve    of    small   central   angle. 
Given     a    3°   curve.       A=2'-/7'. 

uireJ  t0    plot    points    or>    the     curve.    So    opari- 
'too    P.C,    station  0     gives     the    following     values     oi  X.Yand 
C  -for   one    half  of  1he.  curve: 


+50 
+50 


3-  0 
A-3O 
6-  0 
7-30 
9-  0 


5OO 
/OO.O 
S49.8 

199.6 

249.3 
Z38.S 
3*8.0 


Y 


07 

1.1 

/O.S" 

ai 

3?.0 


/oo.o 

If  0.0 
199.9 
249.8 
299.7 
349.5" 


Calling    P.T  station  O     use   the-   same. 
Makes  of  X,  V  and  C     for   the 
other   half  of  the    curve. 


RAILROAD   CURVE  TABLES 


7.    Use    of    long   cKorc/s     m     plotting    a  Transit    line. 
Required    ~)b    plot   the     following    notes: 


Tangent 

Length 

4.79/6 

Total  Angle 

C,   for 
Ttrfo/  Anjte 

f 

I 

SfOO' 
397? 
£800 

5631 

382  €> 
37#4 

28-32'  R. 
I6-/9  L. 
38-44  L. 
4o-54  R 
47-  16  U. 

^8°3ZR. 

12-13  f?. 
26-  3»  L. 
/4-23R 
32-  i-3  L. 

2924.0' 
/2I9.4- 
2628.  » 
/4-J4..6 
3243.4- 

T/ie   length   o/></   angle    of    the 


var/ous 
0/7- 


are    measured,    tiie    total 

?/?</   C,    fa  Hen    from 


tangents 
<j/es 
fatle  //. 

At  o  conyen/en"t  point  or;  ^? 
and  to  a  large  scale  c/ravv  a 
w//A  radivs  of  ^^?9.6S* 

Through     tire     center    z     of    >W  circ/e 
(/row  a    ///>e    parallel    to    tangent  6, 

the    circumference    at  point  t>. 


mop 
circle 


sco/e   to 


circle    YV<?S 
bf  =  2824.0*    ^ 
bq   ~  1219.4     .. 
bh    -  2628./      - 
hK  =   14-34.  6      •• 
bp  -=s  32*3.4     - 
lanyenf  f  para/tel    to    zf 
h  parallel    ib     zh    etc. 

Drow    /engws    of   tangents     1o    scale,    of    map 


wn      lay    off   cA<W$   as  fo//otvs: 
/  b 


.        Jeff 
to/jgefft~ 


poro//e.l   to    z.ej  , 


RAILROAD   CURVE  TABLES 

8.    Use  of   fables  V/   and  VII. 

Table.  V/     ^/Ves    natural   sines    and  cosines    ana    tob/e   VII    nature/ 
fongents   and    cotan gents     to    seven    o'ec.ima/s    -Fpr    angles     varying 
by    Jen    minutes . 

The    maximum    error    resvlfino     from   (//reef     interpolat'ton      or 
intermediate     angles     is     o/?e     u/?//"    in    the     sixth     decmo/  p/ffce 
for   fable.    VI     o/»c/    foc»r     um^s    fer    table.   VII.  Hence.  Kiese  tobies 

are    r»oY&      accurate.      t/?o/f      five-o/ace     tables      vary  Say    by    single, 
minutes. 

Tangents     ore    given    only    for   any/es     under    45°  ana 
for    angles     over    4-5°     since     Jire.ci~    interpolation      /s     not 
m/ssable     outside,     of     these-     Ji/v/ts . 

To    find   the.     tangent    oi    an    a/ty/e    greater    than    45* 
the     reciprocal     of    the    c.oti7r»<jer»t    of    t}»e     angle. 

To  find     the    cotangent    Of     an    angle,     /ess    titan    45"°    take, 
the     recjproco/      of     ^fce     tangent     of    #*e     angle.. 


TABLES. 


TABLE   I.— MINUTES    IN   DECIMALS    OF    A   DEGREE,    AND    LENGTH   OF   A 
ONE-DEGREE    CURVE. 


Mmofes 

of  a 

of  a 
I'  Curve 

Minutes 

Decimals 
of  a 
Degree 

Leng/ft 
of  a 
1°  Curve 

Mnutes 

of  a 
1*  Curve 

r°Corve 

0 

.0000 

O.OO 

2O 

.3333 

33.33 

40 

.6667 

66.67 

.0/67 

1    £7 

2,1 

.3500 

35.00 

41 

.6833 

68.33 

a 

.0533 

3.33 

22. 

.3667 

36.67 

42 

.7000 

7O.OO 

3 

.0500 

ST.  00 

2-3 

.3833 

38.  33 

43 

.7/67 

7/.S7 

4 

.0667 

6.67 

24 

.4-000 

40-00 

44 

.73J3 

73.33 

9 

.0833 

d.33 

.4/67 

4-1.67 

45 

.7500 

7X00 

.1000 

/O.OO 

26 

.4333 

43.33 

46 

.7667 

76.67 

7 

.1167 

11.67 

2-7 

.4500 

45.00 

47 

.7833 

8 

.1333 

13.33 

28 

.4667 

46.67 

48 

.8000 

80.00 

9 

.ISOO 

A£OO 

29 

.4833 

48.33 

49 

.8/67 

81.67 

/O 

.1667 

76.67 

30 

.5000 

50.00 

5X> 

.8333 

83.33 

// 

.1833 

/£33 

3/ 

.5/67 

51.67 

5/ 

.8500 

85.00 

/a 

.20OO 

20.00 

3a 

.5333 

53.33 

52 

-8667 

S£  67 

/3 

2/67 

21.67 

33 

.5500 

55.00 

53 

.9833 

88-33 

!2333 

23.33 

34- 

.5667 

56-67 

54- 

.9000 

9O.OO 

/5 

.£500 

25.00 

35 

.5833 

58.33 

55 

.9/67 

91.67 

/  G 

.2667 

26.67 

36 

.600O 

6OOO 

56 

-93J3 

93.33 

17 

.2833 

28.33 

37 

.6/67 

6/.67 

57 

.9500 

95.00 

18 

.3000 

30.00 

39 

.6333 

63.33 

58 

.9667 

19 

.3/67 

31.67 

39 

65  OO 

59 

.9833 

90.33 

POSITIVE  CORRECTION    FOR    LENGTH     OF  SUB-CHORD     FOR   A  10*  CURVE. 

T/;e  correc'/on  varies  as  the. 
square  of  $e  c/e.gnee  of  curve. 

Thus  for  a  15°  curve  e7/?o/ 
soA-c/joro7  of  7&  /^e  correction 


10 


TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

0° 

r 

T 

E 

C 

M 

X 

Y 

T 

E 

c 

M 

y 

Y 

0 

o.oo 

o.ooo 

o.oo 

o.ooo 

000 

0.000 

50.00 

0.2/8 

IOO.OO 

OZI8 

roo.oo 

0.873 

1 

0.83 

o.ooo 

/.67 

o.ooo 

1.67 

o.ooo 

50.84 

0.226 

01.67 

0.226 

0/.66 

0.902 

2 

/.67 

o.ooo 

3.33 

o.ooo 

3.33 

O.OOI 

5/.67 

0.233 

03.33 

O.233 

05.33 

0.932 

3 

2.50 

O.OOI 

5.00 

O.OOI 

S.OO 

0.002 

52.  SO 

0.241 

OS.  00 

0.241 

0500 

0.962 

4 

3.33 

O.OOI 

6.67 

O.OOI 

6.67 

0.004 

53.34- 

0.248 

06.67 

0.248 

06.66 

0.993 

5 

4.)7 

0.002 

8.33 

0.002 

9.33 

0.006 

S4-.I7 

0.256 

08.33 

0.2^6 

08.33 

/.024 

6 

5.00 

0.002 

/O.OO 

O.O02 

/O.OO 

0.009 

55.00 

0.264 

10.00 

0264 

09.99 

1.056 

7 

5.  83 

0.003 

11.67 

O1003 

11.67 

O.OIZ 

55.84 

0.272 

11.67 

0.272 

1166 

1.088 

8 

6.67 

O.004 

13.33 

0.004 

13.33 

0.016 

56.67 

0290 

13.33 

O.?80 

13.33 

A/2/ 

9 

7.50 

0.005 

IS.OO 

O.OO5 

15.00 

O.020 

57.50 

0.283 

fs.oo 

0.289 

14.99 

1.154 

10 

9.33 

O.OO6 

/6.67 

O.OO6 

16.67 

0.024 

59.  34 

0.297 

116.67 

O.Z97 

116.66 

I.I  88 

II 

9.17 

O.007 

19.33 

0.007 

19.33 

0.029 

59./7 

0.306 

18.33 

0306 

18.33 

1.222 

12. 

10.00 

0.003 

20.00 

0.009 

2o.oo 

0.035 

60.00 

0.3/4 

20.00 

0.3/4 

19.99 

1.257 

13 

10.83 

o.o/o 

ZI.67 

O.O/O 

21.67 

0.041 

60.84 

0.323 

21.67 

a  32  3 

21.66 

1.292 

14- 

It.  67 

0.012 

23.33 

0.0/2 

23.33 

0.048 

61.67 

0.332 

23.33 

0.332 

23.33 

1.327 

If 

12.50 

0.0/4 

25.00 

0.0/4 

25.00 

0.055 

62.50 

0.341 

25.00 

0341 

24.99 

1.364 

16 

/3.33 

0.016 

26.67 

O.O/6 

26.67 

0.062 

63.34 

0.350 

26.67 

0.350 

26.66 

1.400 

17 

14.17 

O.OI8 

28.33 

0.0/8 

2933 

0.07O 

64.17 

0.359 

28.3? 

0.359 

28.32 

1.437 

18 

15.00 

0.020 

30.OO 

0.020 

3O.OO 

0.079 

65.00 

0.369 

30.00 

0.369 

29.99 

I47S 

19 

15.93 

0.022 

J/.67 

0.022 

31.67 

0.088 

65.94 

0.378 

31.67 

0.378 

31.66 

1.513 

20 

16.67 

0,024 

33.33 

0.024 

33.33 

0.037 

66.67 

0.388 

133.33 

0.388 

133.32 

I.5S-I 

2/ 

/7.50 

0.027 

35.00 

0.027 

35.00 

O./07 

67.50 

O.398 

35.00 

0.398 

34.99 

I.59O 

22 

19.33 

0.029 

36.67 

0.029 

36.67 

o.m 

69.34 

0.408 

36.67 

0.408 

36.66 

1.630 

23 

19.17 

0.032 

38.33 

0.032 

38.31 

0.128 

69.17 

0.418 

38.33 

0.4/8 

38.32 

1.670 

24 

20.00 

0.035" 

40.00 

0.035 

4O.OO 

0.140 

70.0O 

0.419 

4o.oo 

O428 

39.99 

1-7/0 

25 

20.93 

0.038 

41.67 

0.038 

41.67 

0.152 

70.94 

0.438 

41.66 

0.438 

41.65 

1.75-1 

26 

ZI.67 

0.0  A  1 

43.33 

0.04/ 

43.33 

0.164 

71.67 

0.448 

43.33 

0.448 

43.32 

1793 

27 

22.50 

0.044 

45.00 

0.044- 

45.00 

0.177 

72.50 

0.459 

45.00 

0.459 

44.99 

1-935 

28 

23.33 

0.048 

46.67 

0.048 

46.67 

0.190 

7*34 

0.469 

46U 

0.469 

46.65 

1.877 

29 

24.  )7 

0.051 

49.33 

0.05/ 

48.33 

0.204 

74.  1  7 

0.480 

48.33 

0.480 

4932 

I.9ZO 

30 

25.00 

0.0  SS 

50.00 

0.055 

50.00 

0.218 

7f.0l 

0.49/ 

1  50.00 

0.49  / 

149.98 

1.963 

3/ 

2583 

0.059 

51.67 

0.058 

5/.S7 

0.233 

75.94 

0.502 

5J.66 

0.502 

51.65 

2.007 

32 

26-67 

0.062 

53.33 

0.062 

53.33 

0.248 

76.67 

0.5/3 

53.33 

0.5/3 

53.32 

2.052 

J3 

27.50 

0.066 

55.00 

0.066 

55.00 

0.264 

77.51 

0.524 

5500 

0.524 

54.98 

2.096 

34 

28.33 

O.O7O 

56.67 

0.070 

56.67 

0.280 

78.34 

0.536 

56.66 

0.535 

56.65 

2.I4Z 

35 

29./7 

0.074 

58.33 

O.074. 

58.33 

0.297 

79.17 

0.547 

58.33 

0.547 

58.32 

Z.I98 

36 

30.00 

0.079 

60.00 

0.079 

60.00 

0.3/4- 

20.01 

0.559 

60.00 

0.559 

59.98 

2.234 

37 

30.93 

0.093 

6/.67 

0.083 

6/.67 

0.332 

90.94 

0.570 

61.66 

O.57O 

6/.65 

2.281 

3* 

31.67 

0.088 

63.33 

0.099 

63.33 

0.350 

91.67 

0.582 

63.33 

0.582 

63.3; 

2.328 

39 

32.50 

0.092 

65.00 

0.092 

65.00 

0.369 

92.51 

0.594 

65.00 

0.594 

64.98 

2.376 

40 

33.33 

0.097 

66.67 

0097 

66.67 

0.388 

83.34 

0.606 

166.66 

0.606 

166.65 

2.424 

4' 

34.17 

0.102 

68.33 

0./02 

68.33 

0.408 

84.17 

0.618 

69.33 

0.6/8 

68.31 

2-473 

4-2 

35.00 

O.IO7 

70.00 

O./O7 

70.00 

0.428 

95.01 

0.631 

70.00 

0.630 

69.98 

"2.522 

43 

35.93 

0.//2 

7/.67 

O.//2 

71.67 

0.448 

85.94 

0.643 

7166 

0.643 

7A64 

2.572 

44 

36.67 

0.117 

73.33 

O.I  17 

73.33 

0.469 

86.67 

0.656 

73.33 

0.655 

73.31 

2.622 

45 

37.50 

0.123 

75.00 

0.123 

75.00 

0.49/ 

97.51 

0.668 

75.00 

0.668 

7498 

2.672 

46 

39.33 

0.129 

76.67 

0.129 

76.67 

O.5/3 

89.34 

O.68/ 

76.66 

068/ 

76.64 

2.124 

47 

39.17 

0.134 

78.33 

0.134 

78.33 

0.5J5 

89.17 

0.694 

78.33 

0.694 

78.31 

2.775" 

4? 

40.00 

0./40 

80.00 

O./4O 

80.0O 

0.559 

90.01 

0.707 

79.99 

0707 

79.97 

2.927 

49 

40.93 

0.146 

S/.67 

0./46 

81.66 

0.582 

90.84 

0.72O 

81.66 

0.720 

91.64 

2.880 

50 

41.67 

0.152. 

83.33 

0./52 

93.33 

0.606 

91.68 

0.773 

183.33 

0.733 

183.30 

2  9?3 

5/ 

42.50 

0.1*8 

85.00 

0./58 

85.00 

0.630 

92.51 

0.747 

84.99 

0.74-7 

94.97 

2.987 

52 

43-33 

0.164 

86.67 

0./64 

96.66 

0.655 

93.34 

0.76O 

86.66 

0.76O 

86.64 

3.041 

53 

44.  17 

0.170 

88.33 

0.1  70 

88.33 

0.68  / 

94.18 

0.774 

88.33 

0.774 

88.30 

3.095 

54 

45.0O 

0.177 

9O.OO 

0.177 

90.00 

0.707 

95.01 

0.788 

89.99 

6.738 

89.97 

3./50 

55 

45.83 

0.193 

91.67 

0.183 

91.66 

0.733 

95.84 

0.902 

9A66 

0.802 

91.63 

3.206 

56 

46.67 

O.I  90 

93.33 

0.190 

93.33 

0.76O 

96.68 

0.816 

93.33 

0.8/6 

93.30 

3.262 

57 

47.50 

0.197 

95.00 

0.197 

95.00 

0.788 

97.  SI 

O.830 

94.99 

0.830 

94.96 

3.3/8 

58 

48-34 

0.204 

96.67 

0.204 

96.66 

0.8/6 

93.34 

0.844 

96.66 

0.844 

96.63 

3.375 

59 

49.  17 

0.211 

98.33 

0.211 

98.33 

0.844 

99.18 

09S8 

98.33 

O.858 

98.30 

3.432 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CUR V  K 


11 


2° 

3° 

/ 

T 

E 

c 

M 

X 

y 

T 

E 

C 

M 

X 

y 

100.01 

0.873 

199.99 

0373 

199.96 

3.490 

|5"o.o4 

1.964 

Z.9997 

1.963 

299.87" 

7.8SZ 

O 

00.85 

0.887 

20/.G6 

0.887 

201.63 

3549 

50.87 

1.986 

30/64 

\.99S 

301.53 

7.94-0 

\ 

01.68 

0902 

03.33 

0.902. 

03  29 

3.608 

51.70 

2.008 

03.30 

2.007 

03.20 

9.02.8 

i 

02.5-; 

0.9  J  7 

04.99 

0.917 

04.96 

3.667 

52.54 

2.O30 

04.97 

2.029 

04.86 

3.116 

3 

03.35 

0.3  32 

06.66 

0.932 

06.62 

3.727 

55.37 

2.052 

06.63 

2.052 

06.52 

8.2of 

A- 

04-.  18 

0.947 

08.32 

0.947 

08.29 

3.787 

54.2  1 

2.07S 

08.30 

2.074 

08.19 

Z.Z9A 

5 

05.01 

0962- 

03.99 

0962 

09.96 

?-84.8 

55.04 

2.097 

09.97 

2.096 

09.85 

9.384 

6 

05:85 

0378 

11.66 

0977 

/A  62 

3.909 

55.97 

2.120 

11.63 

2.  1  19 

11.52 

9.4,75 

7 

06.68 

0.993 

13.32 

0.993 

13.29 

3.97/ 

•F6.7/ 

2.143 

13.30 

2.14-i 

13.  IB 

9.566 

8 

07.51 

I.oo9 

14.99 

1  ooy 

14-95 

4-.013 

57.54 

2.l(,(, 

I4-.96 

2.165 

14.85 

9.657 

9 

}  09.3  5 

1.024- 

21666 

1.02.4 

2/6.62 

4.096 

158.38 

2.1  3d 

316.63 

2.188 

3/6.51 

9.749 

to 

09.18, 

I.O4O 

13.12 

1.040 

18.  28 

4.159 

59.21 

2.212 

Id.  30 

2.211 

19.17 

8.94-1 

n 

IO.OI 

/.OS  6 

19.99 

I.OS6 

/9.95 

4  223 

60.04- 

2.235 

J9.9(, 

2.234 

I9.V4 

8.934 

12 

10.95 

1.072. 

21.66 

1.072 

ZI.6I 

4.287 

60.88 

2.258 

21.63 

2.257 

2150 

9.027 

13 

II.  68 

/.089 

23.3Z 

I.03Z 

23.28 

4.352 

61.71 

2.282 

23.29 

2.2?/ 

Z3./7 

9.121 

14 

/Z.52 

/./Off 

24.99 

I.lo4 

24.95 

4.4/7 

62.55 

2.305 

24.96 

2.304 

24-33 

9.2/F 

15 

/3.?5 

I./2I 

2665 

1.121 

26.61 

4.483 

63.38 

Z.129 

26.63 

2.328 

26.49 

9.310 

16 

A4./8 

l.i  '39 

28.32 

1.137 

28.28 

4.549 

64-.2I 

1.353 

28.29 

2.352 

Z8.l(, 

9.405 

17 

/5T02 

/./S4 

29.99 

1154 

29.94 

4.6/6 

65.05 

2.377 

29.96 

2.376 

29.82 

9.501 

18 

/5.85 

1.171 

31.65 

A/7/ 

3/.6Y 

4.683 

65.  88 

2.401 

3/.6Z 

2.400 

3S.49 

9.597 

19 

/  /6.69 

//#9 

232.32 

1.188 

233.27 

4.7  f/ 

166.72 

?.425 

333.29 

2.424 

333./S 

9.694 

20 

(752 

I.ZOS 

J4-.99 

l.2o? 

34.94 

4.8/9 

67.55- 

2.449 

34.96 

2.448 

34.81 

9.791 

21 

1835 

/222 

36.65 

1.222. 

36.60 

4.887 

68.38 

2.474 

36.62 

24-73 

36.48 

9.888 

21 

13.19 

/  24O 

38.32 

I.Z39 

38.27 

4.956 

69.22. 

2.498 

3829 

2.4-97 

38/4 

9.987 

23 

20.02 

1.257 

39.99 

A  2  57 

39.93 

£026 

70.0? 

2.52J 

39.95 

2.522 

39.90 

10.09 

24 

20.85 

1.274- 

4-1.65 

1.274- 

41.60 

5.096 

70.99 

2.54g 

41.62- 

2.547 

41.4-7 

10.18 

25 

2/.69 

1.292 

43.32. 

1.Z92 

43.26 

5.166 

71.72 

2.573 

43.29 

2.572 

43.13 

10.28 

26 

2Z.52 

1.3/0 

44.98 

1.3/0 

44.9/ 

5.237 

72.55 

2.598 

4495 

2597 

44.80 

10.39 

27 

23.35 

1.329 

46.65 

1.327 

46.59 

5.309 

73.39 

2.62,3 

46.62 

2.622 

46.46 

M.4S 

28 

24-.  19 

/.346 

48.32 

1345 

48.Z6 

5.38  / 

74.  Z2 

2.64$ 

48.28 

2.647 

48.  tZ 

to.  59 

29 

125,02 

1.364 

249.98 

1.364 

24992 

5.4-53 

;  75:06 

2.674- 

34995" 

2.672 

349.79 

10.69 

30 

as.  86 

/.3g2 

51.65 

1.382 

si.  5-9 

5.526 

75.  89 

2.699 

51.62. 

2698 

51.4-5- 

10.79 

31 

26.69 

l.4&o 

53.  32. 

l.4oo 

53.25 

5.600 

76.72 

2.725 

53.28 

2.7^4 

53.11 

10.89 

32 

27.Hl 

/.4/9 

54.98 

1.419 

54-92 

5.674 

77.56 

2.7S-/ 

54.95 

2.7*9 

54.7? 

JA9* 

33 

28-36 

1.4-19 

-56.65 

1.437 

56.58 

5.74-3 

78.39 

2.776 

56.61 

2.77f 

56.44- 

II./O 

34 

29./9 

/.456 

58.31 

1.4  56 

58.1S 

5.823 

79.23 

2.903 

58.29 

2.901 

5810 

//.ZO 

35 

30.02 

1.4-75 

59.98 

1.475 

59.91 

5898 

80.06 

2.829 

59.95 

2317 

59.77 

//.3I 

36 

30.86 

1.494 

6I.& 

1.434. 

61.58 

f.974 

80.90 

2.85  f 

6/.6I 

2.854 

(,1.4-3 

'/.4I 

37 

J/.69 

1.513 

6331 

1.513 

6*24 

6.050 

91.73 

2.881 

63.28 

2.880 

63.09 

//.  Si 

38 

52.55 

/.S32 

64.98 

1.532 

64.91 

6.127 

82.56 

2.908 

64.94 

2.906 

64.76 

H.6Z 

39 

J33.36 

1.55-2 

266.65 

1.5  SI 

266.57 

6.205 

|8?.40 

2.934- 

3*6.67 

2.933 

366.42 

11.7) 

40 

34.  /9 

I.S7/ 

60.  31 

1.571 

69.-z.4- 

6.282 

8423 

2.961 

68.27 

2.960 

68.08 

11.84 

41 

75.03 

/.S9I 

69.98 

1590 

69.90 

6.36  1 

85.07 

2988 

69.94 

2.987 

69.7S 

11.94 

42 

35.96 

1.6  II 

7/64 

1.610 

7/.S7 

6439 

9£90 

3.0/5 

7/.6I 

3.014 

7/.4/ 

I2.0S 

43 

36.69 

1.630 

73.31 

t.63o 

73.Z3 

6..5V9 

86.74 

704-2 

73-17 

3.0*1 

73.07 

12.16 

44 

37  53 

l.65o 

74.99 

1.650 

74.90 

6.598 

87.^7 

3.069 

74.94 

3.06,9 

74.74 

/2.Z7 

45 

38.36 

/.670 

76.64 

1.670 

76.  5& 

6.679 

88.40 

3.097 

76.60 

3.095 

7640 

/2.38 

46 

39.  /9 

1.691 

78.31 

/.690 

78:23 

6.759 

89.24 

3.|24 

79  27 

3.123 

78.06 

12.4,5 

47 

40.03 

1.7/1 

79.98 

1.710 

79.  89 

6.940 

90.07 

3.152 

79.94- 

3.150 

79.73 

12.  6O 

48 

40.96 

/.73I 

81.64 

17  3  1 

81.56 

6.92? 

90.91 

3.190 

9i.6o 

3.178 

S/.39 

12.71 

49 

14-1.70 

1.751 

Z83.3/ 

175-1 

2S3.22 

7.004 

191.74 

3.207 

383.27 

3.206 

383.  of 

£32 

SO 

4-2.53 

1.773 

94.97 

1.7  72 

04.89 

7.087 

91.58 

3.235- 

84.93 

3.234 

84.72 

12.93 

51 

43.37 

1.793 

86.64 

1.793 

86.55 

7.170 

93.4-1 

3263 

t60 

3.262 

86.38 

13.04. 

52 

44.20 

/8/4 

88.31 

1.314 

88.Z2 

7254 

94.24 

3292 

26 

3.290 

88  o4 

'3.16 

5? 

45.03 

/S3S 

89.97 

1835 

89.08 

7.338 

95.08 

3.32O 

89.93 

3.3/9 

$9'.7O 

'3.27 

54 

45.87 

1.157 

91.64 

1356 

9  154 

7.4-22 

95.91 

3.348 

9/.60 

3.347 

91.37 

13.38 

55 

46.70 

1.978 

93.31 

1.977 

93.ZI 

7.507 

9675 

3.377 

93£6 

3.37S 

93.03 

13.50 

56 

47.53 

1-399 

94.97 

1.993 

9  4  .87 

7.533 

97.58 

3.406 

94.9  J 

3-404 

9469 

/1.6I 

57 

48.37 

I.9ZI 

96.64 

1.920 

96.54 

7.679 

99.42 

3.4-34- 

96.59 

34X 

96.35 

13  73 

58 

49.20 

/.  942 

38.30 

/.94Z 

98.20 

7.765 

9925 

3.46? 

98.26 

?,«*/ 

9?pt 

'A'* 

59 

1:2 


TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

4° 

5° 

T 

E 

c 

M 

X 

y 

T 

E 

C 

M 

X 

Y 

0 

200.08 

3492 

399.^2 

3.49o 

39968 

13.96 

250.IG 

5.459 

499.85 

5453 

499.37 

21.90 

1 

00.92 

J  522 

40/59 

3.520 

401.34 

I4-.07 

Sl.oo 

5.4-95 

50/.5/ 

5.490 

501.03 

2I.9S 

2 

0/.7f 

3.551 

03.  ?6 

3.549 

03.01 

/4./9 

51.31 

-5532 

oJ.  /  B 

5.526 

02  69 

2lp9 

3 

02.59 

3.590 

04.92 

3.S39 

0467 

/4.3/ 

52.67 

5568 

04.84 

5.563 

04.35 

Z2.Z4 

4 

0342 

3.6/0 

06.59 

3.608 

06.33 

M.43 

53.50 

5.605 

06.51 

S.600 

0601 

22.39 

5 

04.26 

-?.64o 

08.25 

3.637 

0799 

/454 

54W 

5642 

08.17 

5637 

07.67 

22.54 

6 

05.09 

3669 

09.92 

3.667 

O9.66 

/4.66 

55.  /  7 

5.679 

09.84 

5.67* 

09.33 

Z2.<# 

7 

05.92 

3.699 

//.58 

3.697 

11.32 

14.78 

56.01 

5.717 

11.50 

5711 

10.99 

2?.»3 

06.76 

3.72? 

/3.25 

3.727 

'2.98 

1490 

Sb.84 

5.752 

13.17 

5.748 

72.6? 

22.98 

0759 

3.760 

/4.9/ 

3.757 

/464 

15.02 

S7.68 

5.797 

14.93 

5.78  S 

14.31 

23.13 

IO 

208.43 

3.790 

4-16.58 

3.787 

4/6.3o 

\5.)4 

2585' 

.f.?29 

5  16.  So 

5823 

5/5.97 

23.28 

n 

09.26 

3.820 

'8.25 

3.8/8 

1797 

,15.2.7 

59.35 

5.867 

18.16 

5861 

17.63 

23.43 

12 

10.10 

3.85X 

/9.9I 

3848 

19.63 

15.39 

60.18 

5.9^4 

19.83 

5898 

'9.2') 

23.58 

13 

IO.93 

3-887 

2153 

3879 

2129 

15.  SI 

61.02 

5942 

21.49 

5936 

20.95 

23.73 

14 

11.77 

S.9/Z 

23.24 

3.909 

22.95 

15.6? 

61.95 

5^90 

23.16 

5.927 

22.6' 

23.88 

15 

12.60 

3.943 

24.91 

3.940 

24.62 

/5.76 

62.69 

6.0/9 

24.83 

6.0/2 

24.27 

24.04 

IB 

13.43 

3.9** 

26.57 

3.971 

26.28 

'5.88 

63.52 

6.057 

26.49 

6.050 

2593 

24./9 

17 

14.27 

4-.005 

28.24 

4.002 

2794 

/6.OO 

64.36 

6.095 

28.15 

6.089 

27.59 

#.34 

18 

IS.fO 

4.0i6 

29.90 

4033 

29.60 

/6.J3 

65.  19 

6.734 

2982 

6./27 

29.25 

245o 

•9 

1*94- 

4.063 

3/.57 

4065 

3X26 

16.25 

66,03 

6.173 

37.4* 

6./66 

30.91 

24.6S" 

2.0 

216.77 

4.099 

43324 

4.096 

432.9? 

16.38 

266.06 

6.211 

533.AT 

6.20S 

532.57 

248o 

i\ 

17.61 

4.131 

34,90 

4MB 

J4-.59 

16.51 

67.70 

6.250 

34.8/ 

6.243 

3423 

24.96 

2.2. 

»8.44 

4.163 

36.57 

4.159 

3625 

16.63 

68.53 

6.289 

36.48 

6.282 

35.89 

25.12 

23 

19.28 

4.194 

33.23 

4.191 

379/ 

16.76 

69.37 

6.328 

38.  /4 

6.3P/ 

3755 

25.27 

24 

20.11 

4.226 

39.90 

4.223 

39.57 

16.89 

70.20 

6.368 

39.8/ 

6.367 

39.21 

25.43 

25 

20.95 

4.259 

4/56 

4.255 

41.23 

17.01 

7/.04 

6Ao7 

4/.47 

(,400 

40.87 

2559 

26 

21.78 

A.&l 

43.23 

4.2g7 

4230 

/7.I4 

7/.87 

6.447 

4-3.14 

6.439 

42.53 

25.74 

27 

22.61 

4.323 

44.89 

4.320 

44.56 

17.27 

72.71 

6.486 

44.80 

6.479 

44-.»9 

25.90 

28 

23.45 

435S 

46.56 

4.?52 

46.22 

17.40 

73.54 

6.526 

46.47 

6.5/9 

4-5.84 

26.06 

29 

24*8 

4.388 

48.22 

4.385 

47£8 

'7.5} 

7438 

6.566 

48.13 

6.558 

47.5o 

26.2? 

30 

225.  It 

4421 

4-49.89 

4-.4-I7 

449.  54 

17.66 

275-.2I 

6606 

5W.80 

6.598 

S49.K, 

26.38 

31 

25.95 

4.4*4 

51.56 

4.450 

5/.20 

17.79 

76.0* 

6.646 

5-1.46 

6.638 

50.82 

26.54 

32 

26.79 

4.4-87 

53.22 

448J 

52.87 

17.93 

76.99 

6.686 

53.13 

6.679 

52.48 

26-70 

33 

276* 

•4.52O 

54.89 

4.5/6 

54.53 

15.06 

77.72 

6.727 

54.79 

6.7/9 

54.  14 

26.86 

34 

28.46 

4.553 

56.  55 

4.54.9 

56.19 

IB.19 

79.56 

6.76-7 

56.45 

6.7S9 

S5.SO 

27.01 

35 

29.29 

4.586 

58.22 

4.5S^ 

5785" 

18.32 

79.39 

6.808 

58./Z 

6.800 

57.46 

21.18 

36 

30.  13 

4.620 

5988 

4.6/6 

59.  5V 

1846 

80.23 

6.849 

59.78 

6.840 

59.12 

27.35 

37 

30.96 

4.653 

6/.55 

4.649 

6/./7 

/8.S9 

8/.O6 

6.890 

6/.45 

6.881 

60.77 

275/ 

33 

37.80 

4.687 

63.21 

4)683 

62.83 

18.72 

81.90 

6.930 

63.  // 

6.92? 

62.43 

2767 

39 

32.63 

4.721 

6488 

4.7/7 

64.50 

18.96 

82.73 

6.972 

64.75 

6.963 

64.09 

27.84 

40 

233.47 

4.755 

466.54 

4.757 

466.16 

18.99 

2J33.S7 

7.0/3 

-5-66.44- 

7004 

565.75 

28.00 

4i 

34.30 

4.789 

69.ZI 

47P5- 

67.82 

19.13 

«4.4o 

7.0S4 

68.  H 

7.046 

67.41 

2*.I6 

4E 

35.  13 

4.923 

69.87 

4.819 

69.48 

19.2.7 

85.24 

7.036 

69.77 

7.087 

69.07 

28.33 

4-3 

35.97 

4857 

7/.S4 

4.853 

71.14- 

19.40 

96.07 

7.137 

71.44 

7.122 

70.73 

2350 

44 

36.80 

4391 

73.20 

4.887 

72.^0 

/9.S4 

96.91 

7.179 

73.10 

7.170 

72.38 

2S.66 

4-5 

3764 

4.926 

74.07 

4.922 

74.46 

(9.68 

67.74 

7.2ZI 

74.77 

7.212 

74.04 

2993 

46 

39.47 

4.96  / 

76.  54 

4956 

76.12 

/9.82 

88518 

7.263 

76.43 

7.254 

7S.70 

£900 

47 

39.  3  1 

4.995 

79.20 

4.99/ 

7778 

/9.96 

#9.42 

7.305 

78.10 

7.296 

77.36 

29.16 

48 

40.14- 

5.*3o 

79.06 

5.026 

7944 

20.09 

90.?  5 

r.iA7 

79.7<, 

7.330 

79.02 

2933 

49 

40.98 

5.065 

81.53 

5.06/ 

91.11 

20.23 

41.09 

7.389 

31.42 

73*0 

80.68 

29.50 

5-0 

241.31 

5.  loo 

483.20 

5.0^6 

492.77 

£0.37 

2.91.92 

7.432 

583.09 

7422 

502.33 

29.67 

SI 

42.65 

5.  136 

84.86 

5.131 

84.43 

20.52 

92.76 

7.474 

84.7S 

7.465 

83.99 

W.84 

52 

43.48 

5.171 

86.53 

5./66 

86.09 

20.66 

93.59 

7.5/7 

86.41 

7.507 

85.6$ 

3o.oi 

53 

4432 

5.207 

88.  19 

5.202 

37.7J- 

208o 

94.43 

7560 

88.08 

7.550 

87.31 

30.18 

54 

45.15 

5-242 

89  36 

5.237 

89.4/ 

20.94- 

95".26 

7603 

89.75 

7.593 

83.97 

30.3? 

-#• 

45.99 

5.278 

9/.52 

5.273 

91.07 

21.08 

96  to 

7646 

9/.4/ 

7.636 

90.62' 

30.52 

56 

46.82 

5.3/4 

93J9 

5.309 

32.73 

21.23 

96.94 

7.689 

93-^8 

7679 

92.28 

30.69 

57 

4766 

5.350 

9485 

5.345 

94.39 

21.37 

97.77 

7.732 

94.74 

7.722 

93.94 

30.87 

59 

48.49 

5-386 

96.52 

5.38; 

36.05 

Zi  51 

9&6/ 

7.776 

96.40 

7765 

95.60 

3/04 

59 

49.3? 

5.422 

98.  1  8 

5.4/7 

tt?! 

2/66 

99.44 

7.8/9 

98.07 

7.809 

97.25 

3/.ZI 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


6° 

7° 

/ 

T 

E 

C 

M 

X 

Y 

T 

E 

c 

M 

X 

Y 

300.29 

7863 

59973 

7.052 

598.91 

31.39 

*S0.44 

10.71 

699..F7 

/0.69 

698.Z? 

42.71 

O 

01.11 

7-907 

601.40 

7.896 

600.57 

3/.S6 

5V.  29 

10.76 

70/.24 

10.74- 

99.92 

42.91 

01.35 

7.9f/ 

O3.o6 

794o 

02.13 

3i.n 

52.  // 

10.91 

0290 

/0.79 

701.58 

43.12 

a 

02.79 

7935 

04.73 

7.98^ 

03.99 

Jl.91 

52.9IT 

/0.96 

04.56 

0.94 

03.23 

A3.  32 

3 

03.62 

8.039 

06.39 

R028 

05.54 

32  09 

53.70 

/04I 

06.23 

0.89 

04-.& 

4-3.52 

4 

04.46 

9.083 

08.06 

8.072 

07.2,0 

32.26 

5462 

/0.% 

07.89 

10.94 

06.54 

43.  7/ 

5 

OS.  29 

8.129 

09.72 

9.1/6 

08.86 

3;  44 

55.44 

J/.02 

03.  sr 

to  99 

09.19 

43.94 

<P 

06.13 

3  172 

11.38 

8./*l 

10.51 

3261 

56.30 

1/.07 

1/.22 

//.OS 

098? 

44.14 

7 

06.96 

t.Z'7 

I3.o5 

8.205 

/2J7 

&.80 

57/3 

If.  12. 

12.88 

//./O 

11.50 

44,35- 

8 

07.90 

8.262 

I4-.7/ 

8.250 

13.31 

3298 

57.97 

//.// 

/4SS 

t/./5 

t3.)5 

44.56 

9 

303.64 

8.307 

6/6.38 

8.294 

6/S-.48 

33.15 

358.81 

//  Z2 

7(6.  21 

ll.ZO 

14.^1 

44.7£ 

10 

09.47 

9.352 

I9j04 

3.319 

17.14- 

33.3J 

59.64 

//.28 

17.97 

A.2S 

/6.46 

4-4.97 

II 

10.31 

9.397 

>9.7/ 

9.384 

/8.30 

31.51 

60.48 

//.£? 

/9.S4 

//.3/ 

19.12 

4  5-  >8 

12 

11.14 

5.442 

Zi.37 

14JO 

20.44, 

31.63 

61.3? 

It.  39 

21.20 

t/.*6 

/977 

45.39 

13 

11.98 

£.4*7 

23.03 

8475 

2.2  II 

JJ.87 

62.15 

V.43 

2286 

/f4< 

21.4-2. 

45.60 

/4 

1291 

8.533 

24.70 

9.510 

23.77 

^4.06 

62.99 

11.49 

24  Si 

H:46 

Zi.09 

4-5.81 

15 

13.65 

8.578 

26.36 

3.566 

2543 

34X4 

63.83 

U.S4 

2£J9 

//.Si 

Z4-.71 

46.02 

16 

14.49 

£.624 

29.o3 

S.6>/ 

27.08 

34-41 

64.64 

/t.S9 

27.95 

".57 

26.38 

46.2.3 

17 

/S.32 

8.670 

29.69 

8.6S7 

2874 

•34.60 

65.50 

l/.GS 

29.52 

11.62 

28.04 

4644 

18 

16.16 

8.7/6 

31.35 

9703 

30.40 

34.7? 

66.1& 

11.70 

3I./8 

It.  68 

29.69 

46.65 

19 

3/6.99 

8762 

(,33.02 

8.749 

632.05 

34.97 

367/7 

If.  7  5 

732.94 

H73 

731.34 

46.87 

20 

17  83 

8.808 

34.68 

8795 

33.  71 

3SJ5 

68  01 

I/.2I 

34.5-1 

//.78 

33.0O 

47.08 

Zl 

19.67 

3.855 

36.35 

8.941 

3S.S7 

35.34 

6885 

I/.  86 

36.17 

/'.34* 

34.65 

4-7.29 

22 

19  So 

8.901 

38.0f 

8.997 

37.02 

35.52 

69.  6  & 

H  91 

3783 

11.89 

36.30 

47.51 

2.3 

20.  54 

8.348 

39.68 

8.934 

38.68 

35.  71 

7<?.52 

1/97 

39.50 

//.94 

37.95 

47.72 

24 

2/.  17 

8.99  5 

41.34 

8391 

A0.3) 

35.89 

7/.H 

,/2.02 

AU(, 

12.00 

3?.6/ 

47.94 

25 

22  O/ 

904-/ 

43.00 

9.02.7 

A  1.99 

360^ 

7*./9 

12.08 

A2.8Z 

I20S 

4f.26 

49.15 

26 

22.35 

9.088 

44-67 

9.074- 

43.65 

36.21 

7*03 

/2.I3 

A.4-.48 

'2  fO 

42.91 

48.37 

27 

23.  6g 

9.135 

46.33 

9.121 

45.30 

36A5 

73.  £7 

12.  IS 

4(,.IS 

'?.<6 

4456 

4S.S8 

28 

24.52 

9.183 

48.00 

9/68 

4696 

36.64 

74-.  70 

12.24 

4-7.81 

12.21 

46.2? 

48.90 

Z9 

325.35- 

9.230 

(,49.66 

9.215 

649.6? 

36.83 

375.54- 

/Z.29 

74947 

/2.27 

747.87 

49.02 

30 

2&./9 

9-278 

5/32 

9.263 

50.27 

37.02 

76.38 

12  35 

Sl.lA- 

/?.32 

49  SZ 

49.24 

31 

2703 

9.325 

52.99 

93/o 

5/93 

37.21 

77.11 

I2.4O 

S2.80 

12.38 

51.17 

49.45 

32 

27  W 

9.373 

54.65 

9.358 

53.58 

37.40 

78.05 

i*A6 

S44t 

/t.43 

S«?.8J 

49.67 

JJ 

2S.70 

9.42  1 

56.3? 

9.405 

5S.Z4- 

37.59 

78.  V) 

IZ.SI 

56.13 

I2.4J 

5449 

49.89 

JA 

29.53 

9.469 

57.98 

9.453 

f6S9 

37.78 

79.73 

12.57 

5779 

t2.54- 

56.}3 

J&.  It 

35 

30.37 

9.5/7 

59.64 

9.  Sol 

58S5 

3797 

80.56 

S2.62 

5*45 

'2.60 

57.78 

£631 

16 

J/2/ 

9.565 

61.31 

9  5  43 

60.21 

38.16 

QIAO 

/2.68 

6i.li 

I2.(,S 

S943 

505$ 

37 

32.04- 

9.6'3 

62.97 

9597 

61.86 

J8.36 

82.24 

/Z.74 

6i.7$ 

K.  7f 

61.09 

5b>7 

38 

#.« 

9.662 

64.64 

9645 

63.52 

38.55 

83.07 

/2.T9 

^4.44 

IZ.7( 

62.74 

51.00 

39 

33J.7/ 

9.7/0 

616.30 

9.694 

66S~/7 

3S.74 

383.91 

/2.9S 

766.  10 

12.92 

76439 

5722 

40 

34.55 

9.7.T9 

6796 

9.742 

66%3 

.39.94 

84  7S 

/z.90 

67.77 

11.97 

66.04 

57.^4 

41 

te.T) 

9.5og 

69.63 

9791 

6848- 

39.)  3 

£5.59 

12.96 

69.4-J 

1293 

<>7.(>9 

5/66 

42. 

36.22 

9.85-7 

71.29 

9.340 

70.14 

J9.32 

£642 

/3  oi 

71.09 

'299 

&>JS 

57.89 

43 

J7.0& 

9.9o(, 

72.95 

9.888 

7/79 

39.52 

87.26 

13.07 

72.76 

11.04. 

7/00 

52.11 

44 

3790 

9.955 

74.62 

993? 

7345 

J9.72 

88.10 

'J  13 

7442 

13.10 

•72.  (,5 

5,?.H 

45 

38  7) 

10.00 

76.2? 

9.987 

75/O 

39.91 

88.91 

S3./9 

76  08 

/J.i6 

74.  3O 

5^.56 

44 

39.57 

/O.Q5 

7795 

to.  oa 

7676 

4c.lt 

89.77 

/?.?* 

7774 

/1.2> 

75  9  f 

52.79 

47 

4o.4o 

IO.IO 

73.61 

10.09 

7g4l 

4o.3l 

90.61 

/3  3O 

79.0-1 

/3.17 

7760 

53  01 

4g 

4/.24 

10.15 

SI.  27 

IOJ3 

9oo7 

40.  50 

9  /.4S 

/?Jt 

8/.O7 

/3.33 

79.Z5 

53.24 

49 

34-2.09 

10.  2o 

68294 

ioj8 

691.72 

40.70 

J9£28 

/J.4/ 

782  gj 

/3  38 

780  9  1 

5^.46 

5O 

4Z.9/ 

10.25 

84-60 

/02} 

%3.38 

40,90 

93.  rt 

I3A7 

8443 

1344 

8256 

fJ69 

r/ 

4?.  75" 

1030 

8626 

to.29 

&5.0? 

4/./O 

93.96 

/3.S) 

96.06 

13  SO 

$a?-' 

53.92 

52 

44  59 

IO.35 

87.93 

/o.3J  . 

fo.69 

4  /JO 

94.79 

/3S9 

»77? 

I3.K 

tiS-86 

54/5 

S3 

4542 

#.40 

89.  f  9 

'0.& 

98.  w 

4l.fo 

95.63 

/1  64 

8938 

/?.(,< 

87.  $> 

54.39 

54 

4626 

1045 

9/26 

/0*1) 

9o.oo 

4170 

96.47 

/3.7Q 

^1  Of 

13.67 

89/(, 

54  f>l 

5S 

4709 

10.50 

9292 

/0.48 

9l.f,5 

4-1  9o 

9T.3/ 

X3.76" 

91.  7  f 

IS.7) 

9O.9I 

14.84 

56 

47.  9J 

/O.SS 

945? 

/0.53 

9).  11 

42.10 

•9S./4 

/3.&Z 

94  J/ 

//.  7g 

9244, 

5  £07 

S7 

4£77 

10.  (,1 

96.25- 

IO.59 

94% 

42.10 

9?  .99 

13.97 

96.04 

/)34 

94.11 

55.30 

-58 

49  60 

'066 

979/ 

/0(>4 

9662 

42  SI 

9992 

'393 

9770 

13.90 

9576 

SS53 

5? 

11 


TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

8° 

9° 

T 

E 

c 

M 

X 

Y 

r 

E 

C 

M 

X 

\y 

0 

400.66 

/3.99 

799.36 

//96 

797.41 

S5-.76 

450.93 

77.72 

89909 

7766 

896.31 

^.54 

1 

01.4-9 

/4.05 

80J.02 

14.02 

99.06 

*5.99 

SI.  77 

17.78 

900.75 

/7.7* 

579^ 

70.ft> 

2 

02.33 

/4./I 

02.69 

14-07 

800.71 

S6.23 

FZ.bl 

r/7.S5 

02.4-1 

17.79 

99.61 

7/.O6 

3 

05.17 

14.17 

04.35 

14.13 

0236 

XA.6 

5JAS 

17.92 

C4-.07 

'7.36 

901.25 

7/33 

4 

04-.OI 

14.2$ 

06.01 

14.19 

04.01 

56.69 

$4.Z9 

/7.98 

os.  i  y 

17.93 

02.90 

77.59 

5 

04.84 

14.2% 

07.67 

14.25 

05.66 

&.91 

ff./3 

1805 

07.39 

17.99 

04.54 

77.85 

6 

05.68 

tf.34 

09.34 

14.31 

07.31 

57.16 

55.96 

18.11 

09.06 

/8SX> 

06.)9 

7^.  // 

7 

06.  5  a 

14-Ao 

11.00 

14.37 

08.96 

57.40 

S6.80 

'8.18 

10.72 

18.  \2 

07M 

7<?.3g 

8 

0736 

74.46 

12.  66 

M.43 

/0.6I 

5763 

57.64 

18.25 

J2.38 

'3.  19 

05.48 

72.64 

9 

08.19 

#.52 

14.32 

14-49 

I2.i6 

57.87 

58.41, 

J8.3I 

74.04 

78.26 

11.13 

75?.  91 

IO 

409.03 

14.58 

8/5.99 

14.54- 

813.91 

58.10 

459.12 

18.38 

915.70 

/?.# 

9/2.77 

73.17 

II 

09.27 

74.64 

17.65 

I4.(,o 

15.56 

58.31 

60.16 

;&45 

17.36 

'8.39 

14.42 

73.44- 

11 

10.71 

14.70 

19.31 

14.66 

I7.ZI 

S8.S8 

61.00 

18.52 

I9.0Z 

18.46 

16.06 

73.70 

13 

11.54 

14.76 

20.97 

14.72 

IBS6 

58.8Z 

61.84 

IB.S8 

20.68 

18.51 

I7.7f 

73.97 

14- 

12.38 

14.B2 

22.64 

14.78 

20.51 

59.06 

62.67 

18.65 

22.35 

18  59 

/9.35 

74.24 

IS 

13.22 

/4.gff 

24.30 

14.84 

22.16 

59.29 

6351 

/8.7Z 

24.01 

18.66 

21.00 

74.51 

16 

H.06 

1434 

25-96 

I4*)O 

23.81 

5953 

64.35 

18.79 

25.67 

/8.72 

22.64 

74.77 

17 

14.99 

/f.oo 

27.62 

14.96 

25.46 

59.77 

65.13 

18.85 

27.33 

18.79 

2-4.29 

7f-04 

18 

IS.73 

&.<*> 

29.29 

'5-.CZ 

27/7 

60.OI 

66-03 

#92 

28.99 

ISM 

as.9j 

7S.3I 

)9 

16.57 

/S.I2 

30.95 

IS.  OS 

28176 

60.25 

66.97 

18.99 

3o.6f 

/8.93 

27.58 

7S.58 

20 

4-17.41 

&J8 

83261 

1F.I4 

830AI 

60.50 

467.71 

/9.06 

932.31 

1299 

929.22 

75.85 

21 

18.25 

/S25 

34.Z7 

IS.  20 

32.06 

60.74 

f>8.fS 

&.I3 

33.97 

19.06 

30.?7 

76.12 

22 

19.08 

/S.3I 

15.93 

IS.Z7 

33.71 

60.98 

69.39 

/9.I9 

3563 

79.»? 

32.51 

763) 

23 

19.92 

tf.17 

37.60 

/5.33 

35.36 

61.22 

70.22 

19.26 

37.  3O 

19.20 

34.16 

76.  6C 

24 

20.76 

/S.43 

30.26 

/S.39 

37.00 

6/.47 

7/.06 

/9.33 

38.96 

19.27 

35.S0 

7694 

25 

21.60 

tf.49 

40.92 

15.45 

38.65 

61.71 

71.90 

/94o 

40.62 

79.33 

37.44 

77.21 

26 

12.43 

I5-.SS 

4-2.58 

15.  SI 

40.10 

6l-9f 

72.74 

I9A7 

42.28 

79.40 

39-09 

77.4? 

27 

23.17 

15.61 

44.24 

15.57 

41.95- 

6220 

73.58 

/9.54 

4?.94 

19.47 

40.73 

77.76 

2* 

24.11 

/f.67 

45.9  / 

15.63 

43.60 

62.44- 

7442 

/9.6I 

45.60 

19.54 

42.38 

78.03 

29 

24.95 

/S.74 

4.7.S7 

15.69 

45.25 

62.69 

7y.Z6 

/9.68 

47.2.6 

19.61 

44.02 

7g30 

30 

425.79 

15,80 

849.23 

1S.76 

846.90 

62.94 

476.10 

I3.7S 

948.92 

I9.6B 

945.67 

70.58 

31 

26.62 

15.86 

S0.89 

IS.22 

48.59- 

6J.I8 

76.9A 

79.82 

50.59 

19.1  T 

47.31 

78.85 

32. 

2.7.46 

/S.92 

52.56 

'S.88 

So.19 

63.43 

77.  78 

79.89 

-T2.25 

/9.82 

48.95 

79.13 

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29.30 

'5.99 

54.22 

15.94 

51.84 

6368 

78.61 

19.96 

5331 

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50.60 

79.4-1 

34 

29.14 

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SS.88 

16.00 

53.49 

all 

79.45 

Z0.03 

SS.57 

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52.24 

79.68 

35 

29.98 

16.  M 

S7.f4 

/6.07 

SSI/4 

64.17 

80.29 

20.10 

57.23 

20.03 

33.88 

79.96 

36 

30.91 

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SB.  20 

16.13 

5679 

6442 

81.1? 

20.17 

S8.99 

20.09 

5553 

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37 

31.65 

/6.24 

60.87 

16.19 

58.43 

6467 

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20.24 

6o.5S 

20.16 

57/7 

80.5Z 

38 

32.49 

16.30 

62.5) 

/6.2? 

60.08 

64.92 

8Z.8I 

W.3I 

61.21 

20.23 

S8.8I 

80.79 

39 

33.33 

16,36 

64.19 

/6.32 

61.73 

6S-.I7 

83.65 

20.38 

63.87 

20.30 

60.46 

VI.  07 

40 

434.;  r 

I6A1 

365.85 

16.38 

863.38 

65.42 

484.49 

20.45 

965.53 

20.37 

962.10 

St.  3  5 

41 

35.01 

/649 

67.51 

76.44 

6S.oi 

6567 

8533 

20.52 

67/9 

^o.44 

63.74- 

gl.63 

42 

35.94 

76.55 

69.  13 

16.  SI 

66.67 

65.93 

86-17 

20.55 

68.85 

20.  SZ 

65.39 

81.91 

43 

36.6? 

16.61 

70.84 

16.57 

68.32 

66.18 

87.01 

20.66 

70.51 

20.59 

67.03 

92.20 

44 

J7.52 

fc.68 

7250 

16.63 

69.97 

66.43 

87.8  f 

20.73 

72.18 

20.66 

68.67 

82.48 

45 

MX 

/6.74 

74.16 

16.70 

7/.6I 

66.68 

88.69 

10.80 

73.94 

20.73 

70.31 

8276 

46 

39.20 

1631 

75.82 

16.76 

73.Z6 

66.94 

89  S3 

20.87 

7£fo 

Z0.80 

71.96 

83.04- 

47 

4003 

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7748 

16.92 

74.91 

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9o.36 

20.95 

77/6 

20.87 

73.60 

8332 

48 

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/6.94 

79.15 

16.  V) 

76.56 

67.45 

9l.2o 

21.02 

78.82 

20.94 

7S.24 

83.61 

49 

41.71 

17.00 

a>.8/ 

16.95 

7&20 

67.70 

92M 

Z/.09 

80.48 

21.01 

76.98 

83.89 

50 

442.55 

17.07 

982.47 

17.01 

879.85 

67.96 

492.88 

ZI.I6 

982.  14 

21.0$ 

97ff.fi 

84.  18 

ft 

43.39 

17.1-5 

84/3 

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68.21 

93.72 

ZI.23 

83.80 

21.  IS 

80.17 

£4.46 

£2 

4423 

I7.'9 

35.79 

17.14 

83.f4 

68.47 

94.56 

21.30 

£5.46 

Zt.23 

81-81 

»4.75 

S3 

45.06 

I7.2t> 

6746 

1721 

84.79 

68.73 

9S.40 

21.38 

87./2 

Z/.3O 

83.45 

85.03 

54- 

45.90 

17.32 

89.12 

17.27 

86.44 

68.99 

96.24 

2  IAS 

88.78 

2/.37 

95.03 

#5.32 

ff 

46.74 

17.39 

9078 

/7.34 

88.0% 

69.24 

97.08 

21.52 

90.44- 

2/.44 

86.74 

85.61 

S6 

4Z58 

'7.46 

92.44 

17.40 

0973 

69.50 

97.9* 

21.59 

92.10 

21.  SI 

8S.38 

85  89 

57 

4&4Z 

/7.51 

94./0 

17.1(7 

9/.3S 

£9.76 

98.76 

2.1.61 

93.76 

2/.S9 

90.02 

#6.18 

58 

49.26 

I7.S9 

9S.7(, 

n.n 

93.02 

70.02 

99.60 

21.74 

95.42 

2.1.66 

91.66 

86.47 

S? 

50,o? 

17.65 

97.42 

,740 

94,67 

70.28 

&0.4& 

Zt.81 

97.0$ 

21.73 

93.30 

86.76 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


10° 

11° 

/ 

T 

B 

c 

M 

Y 

Y 

T 

E 

C 

M 

X 

Y 

JO/.  28 

2/.89 

938.74 

ZUSO 

99494 

87.05- 

5.57.70 

2kSO 

10983 

26.38 

O93.3 

/05.Z  7 

0 

02.12 

2/.9fe 

looo.q- 

£1.68 

96  SS 

3734 

52.54 

26.58 

noo.o 

26.46 

94.9 

0559 

1 

oz.96 

22.03 

OZ.I 

ZI35 

9«23 

07.6} 

Si.  39 

Z6.66 

01.6 

26.54 

96.5 

05.9/ 

2 

03.80 

22.'/ 

03.7 

22.02 

9287 

87.K 

54.23 

2674 

03.3 

26.6Z 

98.1 

06.23 

3 

04.64 

Z2.I8 

05.4 

22  .09 

/<?0/.5 

98.Z/ 

55:  o  7 

265? 

05.0 

26.70 

99.9 

06.55" 

4 

05.4S 

22.25 

07.1 

2?./7 

<»3./ 

B8.50 

55.9/ 

26  90 

06.6 

26.78 

II  01.  4 

06.97 

5 

06.32 

22.3* 

08.7 

22.24- 

04.8 

9879 

56.75 

26.99 

0g.3 

26.86 

03.1 

07.19 

6 

07.  l(> 

22.40 

lOfl- 

22.3/ 

06.4- 

$9.08 

J759 

27.0  f 

09.9 

26.94 

04.7 

07.51 

7 

08.00 

22.48 

K.O 

22.39 

08.  1 

89.38 

58.43 

27  J  5 

//.£ 

2702 

06.4 

07.93 

g 

08.34 

22.55 

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225% 

09.7 

89.b7 

59.27 

27-2? 

/3.^ 

27./0 

08.0 

08.15 

9 

5Y?9.68 

22.62 

0/5-.3 

22.54 

10  II.  4- 

89.96 

5"6O.// 

27.31 

II  14-3 

Z7./8 

/A>9.6 

108.4-7 

to 

/0.S2 

22.70 

/70 

226/ 

13.0 

90.26 

60.96 

27.39 

16.6 

27.26 

//.  ? 

08.90 

n 

11.3k 

22.77 

/0.7 

22.68 

/4.6 

90.SS 

6  /.go 

27.48 

I8.z 

27.75 

/2.9 

09.  IZ 

12. 

12.20 

22.85 

20.3 

22.76 

/6.3 

Sb.85 

6Z.64 

27.56 

19.9 

27.43 

14.  5 

09.44 

n 

13.04 

22.92 

22.o 

22.83 

/7.9 

91.14. 

63.48 

2764 

21.5 

27.  5/ 

16.2 

09.77 

14- 

13.98 

23.0O 

2*6 

Z2.9I 

/9-6 

9144 

64.32 

27.72 

23.2 

27.59 

17.8 

/0.09 

15 

14.72 

23.0? 

25.3 

22.9? 

2/.2 

9174 

65./6 

27.81 

24.9 

2767 

19.4 

10.4,2 

'16 

IS.5S, 

Si.  IS 

270 

23.06 

22.8 

92.04 

66.00 

27.99 

26.5 

27.75 

Zl.l 

/0.74 

17 

164-0 

33.22 

286 

2J./3 

24.5 

32.33 

66#5 

27.97 

28.2 

27?4 

22.7 

11  .07 

19 

17.24 

2J.30 

*>.  3 

23.20 

26.1 

92.63 

6769 

28.OS 

£9.8 

Z7W 

Z4.3 

11.40 

19 

518.09 

<?3.37 

/03/.9 

23.28 

102.7.8 

9^<)3 

«?.53 

18.14 

I\3I.S 

29.00 

1126.0 

I  If.  73 

20 

18.9  Z 

2,345 

33.6 

2J.35 

29.4 

27.23 

69.  ?7 

28.22 

33.2 

28.08 

27.6 

12.05 

21 

19.76 

23.53 

J5.3 

23.43 

3l.O 

9J.S3 

70.ZI 

28.30 

J4.8 

28.J6 

29.2 

12.38 

22 

20.60 

23.60 

J6.9 

23.51 

32.7 

9^.83 

7/.05 

28.39 

36.5 

ZB.IS 

309 

12.71 

23 

21.44. 

23.6* 

38.6 

23.5? 

34.} 

94.  /3 

7/.9o 

28.4-7 

38.1 

Z8.33 

325" 

13.04 

24 

22.28 

23.7J- 

4o.2 

<a.66 

36.0 

94.43 

72.74 

28.SS 

39« 

28.41 

34.1 

13.37 

25 

23.  /2 

a3.83 

4L9 

23.73 

37.6 

94.73 

7^.58 

2S.64 

4is 

28.50 

35.8 

13-70 

it. 

23.96 

23  .9/ 

43.6 

23.  gi 

39.2 

£5.03 

7442 

23.72 

43./ 

28.58 

37.4 

14.03 

27 

24.80 

23.98 

45.2 

23.  gg 

4-09 

95.34 

75.26 

2S.8I 

44.g 

2866 

39.0 

14.36 

28 

25.64 

24.06 

465 

23.96 

42.5 

95.64 

76.10 

29.89 

46.4 

28.751 

40.7 

14  fd 

29 

526.4? 

24,/4 

to48.5 

24.04- 

P44-.I 

95.94 

576.95 

29.97 

1/4-8.  1 

28.83 

1142.  3 

IIS.OZ 

30 

27.32 

24.2  / 

5o.Z 

S4.ll 

4-58 

96.2S 

77.79 

29  06 

A9.7 

28.9/ 

43.9 

15.36 

31 

2916 

24.29 

51.9 

Z4.Q 

4-7.4 

91.SS 

75.63 

29./4 

S-/.4- 

29.00 

45.6 

15.69 

32 

29.00 

2437 

53.5- 

24.2.7 

49.  / 

96.96 

79.47 

29  23 

5^./ 

29.08 

4-7.2 

16.02 

33 

29.04 

2.4,45 

fff. 

24.34- 

50.7 

97/6 

80.3* 

29.31 

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29.  16 

48.8 

16.36 

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563 

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52.3 

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£9.40 

56.4 

z9.tS 

50.  5 

16.  (Q 

35 

3/.5Z 

2«.6<? 

58.S 

24.50 

54.0 

97.77 

82/JO 

29.4-8 

5-8.0 

29.13 

52.1 

17.03 

3fe 

32.36 

24,69 

60.2. 

24.57 

55.6 

98.08 

82.84 

2957 

59.7 

29.41 

f3.7 

17.36 

J7 

33.ao 

24.T& 

61.8 

24-65 

573 

98.39 

£3.6g 

29.65 

61.3 

29.  50 

55.4 

/7.70 

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34.05 

24  & 

63.5 

3J.7.J 

jy.9 

98.7O 

84.52 

29.** 

63.0 

29.5? 

570 

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39 

534.89 

24.91 

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24  go 

/060.5 

99.00 

585.36 

29.82 

//64.7 

29.67 

11586, 

#37 

4o 

35173 

14.99 

66.8 

24.  S3 

62  .t 

99M 

86.2/ 

29.91 

66.J 

29.75 

6o.3 

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4-1 

36.5-7 

25.07 

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24.96 

63.8 

99.62 

8705 

30.  OO 

68.0 

29.84 

61.9 

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37.4/ 

25.A5 

70.  / 

25.  04 

65.4 

99.93 

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30.08 

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63  S 

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4-3 

38.25 

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^5.)  2 

67.1 

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88.7* 

30.17 

71.3 

30.01 

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44 

39.09 

25.30 

73.4 

25.  /9 

68.7 

00.55 

89.58 

302$ 

73.0 

30.09 

66.8 

20.06 

45 

39.93 

25.3? 

7S.I 

25.Z7 

TOA 

00.86 

90.42 

30.34 

746 

30.18 

68.4 

20.40 

46 

40.77 

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762 

25.35 

72.0 

01.18 

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76.3 

30.27 

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47 

41.61 

2S.54- 

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22.79 

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4&Ct 

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03.37 

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3/.03 

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3o.87 

91.5 

23.14 

54 

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85.1 

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9^.00 

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55 

48.34 

26.  18 

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38.84 

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23.82 

56 

49.  (8 

26.26 

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043i 

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31.13 

86.4 

24.17 

57 

5J.02 

26.34 

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90.0 

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600.51 

3/.38 

94.5 

3l.il 

88.0 

24.52 

58 

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26.42 

9fe.7 

Z630 

9/6 

04.95 

01.37 

3/47 

9fe.2 

3/.30 

89.6 

?4.9<i 

59 

16 


TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

12° 

13° 

T 

E 

c 

M 

X 

Y 

T 

E 

C 

M 

X 

Y 

0 

GCtJLI 

37.56 

1197.8 

3/39 

1191.3 

I25.2/ 

652.S/ 

3707 

1297.? 

36.W 

1298.9 

I46S5 

1 

03.05 

31.65 

99.5" 

3A47 

92.9 

25.55 

53.66 

37.  /6 

98.9 

36.9? 

90.5 

4723 

2 

03.90 

31.74- 

/20U 

3/.56 

94.5 

25.90 

^•457) 

}7S6 

I3oo  S 

37.02 

92.  \ 

47.60 

3 

04.74 

3/.W 

02-8 

J/.65 

96.2 

26.Z5 

5J.34 

37.36 

02.2 

3711 

93.8 

47.95 

4 

oy.s» 

31.91 

04.5 

3f.l4 

97? 

2660 

-^V? 

37.45 

03.9 

3721 

95.4 

48.35 

S 

06.42 

32.00 

06.  1 

31.92 

99.4 

26>5 

57.03 

37.55 

05.5 

37.30 

970 

48.73 

6 

07Z7 

32.03 

078 

3/.9I 

IZOI.O 

27.29 

f788 

37.64 

07.2 

37.40 

98.6 

4-9.11 

7 

09.  // 

32./8 

09.4 

32.00 

02.7 

Z7M 

59.72 

37.74 

083 

37.43 

1300.3 

49.49 

e 

08.95 

32.Z7 

//•/ 

32.09 

04.3 

27.99 

59.57 

37.84- 

10.5 

37.S9 

01.9 

49.84 

9 

».7* 

52.36 

X2.7 

32.18 

or.9 

20.34 

60.41 

3793 

I2.\ 

37.69 

03.5 

,57.24 

)o 

6/0.64 

3245 

/2/4.4 

&.zt 

\207.6 

I28-7O 

661.25 

38.03 

1313.8 

37.78 

13  OS./ 

I&.6Z 

II 

11.48 

32.54 

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3^.^f 

09.Z 

29.05 

62.  (O 

38.13 

»5.4 

37.  gg 

06.7 

SI.OO 

/z 

12.32 

32.63 

/7.7 

32.44 

10.8 

29.40 

62.94 

39.23 

17.1 

3797 

08.4 

5/38 

n 

13.17 

32.72 

/*4 

32.53 

124 

29.75 

63.79 

39.32 

18.8 

3807 

10  0 

5776 

14 

14.01 

32.81 

21.0 

32.62 

14.1 

30.  to 

64.63 

38.4* 

204 

38.  1  6 

11.6 

52.15 

15 

14.95 

32.90 

22.7 

32.  71 

15.7 

30.46 

65.48 

38.52 

22.1 

38.26 

/3.2 

52.W 

16 

IS.69 

52.99 

243 

32.90 

/7.3 

30.8/ 

66.32 

38.61 

23.7 

38.36 

14.9 

52.91 

17 

16.54 

I?.0g 

26.0 

32.9) 

/9.0 

3/J7 

67.  /7 

38.71 

254 

38.45 

16.5 

53.29 

18 
19 

17.38 
19.22 

33.17 
33.26 

27.7 
29.* 

32.98 
33.06 

20.6 
22.Z 

31.52 
31-99 

68.01 
68.86 

38.91 
30.91 

270 
28.7 

3&SS 
38.65 

IB.I 
'9.7 

SSL 

7-6 

619.07 

33.35 

J25/.0 

5/lS 

IZ23.8 

1  32.23 

669.70 

39.01 

1330.3 

38.74 

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A54.44 

Zl 

19.91 

33.44 

32.6 

33.24 

25.5 

32.59 

70.54- 

39.10 

320 

38.84 

23.0 

54.83 

2t 

20.75 

33.H 

34.3 

33.33 

27J 

J2.94 

7/.39 

39.20 

33.7 

38.94 

24.6 

55.  z/ 

23 

ZI.6O 

33.62 

35.9 

33.41 

28.7 

J3.30 

72.23 

39.30 

35.3 

39.03 

26.2 

5560 

24 
25 

22.44 
23.28 

».7/ 
33.80 

376 
39.3 

33.W 
33.60 

30.4 
32.0 

33.66 
34.02 

73.08 
73.92 

39^40 
39.50 

37.0 
38.6 

39.  13 
3923 

27g 
29.5 

55.98 
56.37 

26 

24.13 

33.99 

40.9 

33.69 

3J.G 

3438 

74.77 

39.60 

44.3 

39.32 

31.1 

56.76 

27 

24.97 

33.96 

42.6 

33.78 

J5.2 

34.74 

7S.6I 

39.70 

41.9 

39.4? 

32.7 

57.  If 

28 

25.8  ; 

34.09 

44.2 

33*7 

J6.9 

35./0 

76.46 

39.79 

43.6 

39.52 

34.3 

57.53 

& 

£6.66 

34.17 

45.9 

3-3.96 

38.5 

35.46" 

77.30 

39.99 

45.2 

39.6? 

353 

579? 

JO 

627.50 

34.26 

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34.06 

»24o.l 

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679.15 

39.99 

'346.9 

39.7,? 

1337.6 

158.31 

31 

2S.34 

34.35 

49.2 

34.15 

41.8 

36.19 

79.99 

4009 

4#.6 

39.SI 

39.2 

59.70 

32 

29.  /9 

34  44 

Jfc.9 

34*4 

43.4 

36.54 

79.84 

40.  19 

50.2 

39.9; 

40.8 

59.09 

33 

1003 

3453 

525 

34.33 

45.0 

36.90 

80.69 

40.29 

51.9 

40.01 

42.4 

59.48 

34 

30.87 

34.63 

S4.Z 

34.42 

46.6 

3726 

9153 

40.39 

-5J.5 

40.11 

44.0 

59.87 

35 

3A72 

34.72 

55.9 

34.51 

49.3 

37.63 

92.37 

40.49 

552 

40.11 

45.7 

60.26 

36 

32.56 

J4.?» 

57.5 

34.60 

49-9 

3799 

#3.22 

40.59 

5S.8 

40.31 

47-3 

60.65 

37 

33.40 

34.90 

59.  \ 

34.69 

51.5 

38.35 

8J4-06 

4«69 

59.5 

40.40 

48.9 

61.  05 

38 

34.25 

35.00 

60S 

34.78 

53.1 

3972 

54.91 

40.79 

60.1 

40.50 

-S-0.5 

6/.44 

39 

35.09 

35.09 

624 

34.88 

54.9 

39.08 

95.76 

40.  89 

61.8 

40.60 

52.1 

61.83 

4o 

635:95 

35/8 

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34.97 

1156.4 

139.45 

626.60 

40.99 

1363.4- 

40.70 

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I62-.Z3 

41 

36.7? 

35.  28 

6£  8 

35T06 

58.0 

39.91 

87.45 

4l.o9 

65.  / 

4o.go 

55.4 

62.62 

42 

37.62 

35.37 

674 

35.15 

59.6 

40.18 

88.29 

4/./9 

66.9 

40.90 

57.0 

63.01 

43 

39.46 

35.46 

69.  / 

3S.24 

61.3 

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89.14 

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684 

4/.00 

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63.41 

44 

39.31 

35.56 

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70.I 

41.10 

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63.90 

45 

40.15 

35.65 

72.4 

35.43 

64.5 

41.28 

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4/.50 

71.7 

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41.00 

35.74 

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35.52 

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91.67 

41.60 

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4110 

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6460 

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35.94 

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35.  61 

67.8 

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92.52 

41.70 

75.0 

4/40 

6S-.I 

6499 

48 

4ZM 

35.93 

77.4 

35.71 

69.4 

42.39 

93.36 

41.90 

767 

41.50 

66.7 

65.39 

49 

43.53 

36.03 

79.0 

3S.90 

7f.o 

42.76 

94.21 

41.90 

78.3 

41.60 

68.3 

65.79 

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644.37 

36.12 

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3589 

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143.13 

695.06 

42.00 

1390.0 

4-1.70 

1370.0 

166.19 

5/ 

45.21 

36-ZI 

8^3 

^5-99 

74.3 

43.50 

959o 

42.JI 

91.6 

41.80 

7/.6 

66.59 

52 

4606 

36.31 

§4.0 

J6.Gg 

7S.9 

43.87 

96.75 

42.21 

83.3 

4V.  9o 

73.Z 

66  98 

53 

46^0 

34.40 

56 

36.17 

77.5 

44.24 

97.59 

42.31 

95.0 

4200 

74.  8 

67.38 

54 

47.7^ 

36.50 

87.3 

36Z7 

79.  / 

44.61 

98.44 

42.4  / 

86.6 

42.10 

76.  .4 

67.78 

55 

4«.» 

36.59 

!*.9 

36.36 

80.8 

44.98 

99.28 

42.51 

88-3 

42.20 

78.0 

68.18 

J"6 

49.43 

36.69 

9fl6 

3645 

824 

4*.3J 

700.  /  3 

426? 

89.9 

42.30 

79.7 

68.59 

57 

AJEI 

36.71? 

9EJ 

36.55 

P4.o 

45.7* 

00.98 

42.72 

91.  6 

42/W 

81.3 

68.99 

58 

5/./Z 

3fe98 

93.9 

J664 

856 

46-10 

0/.8Z 

42.82 

93.2 

42.51 

92.9 

6939 

5? 

5A97 

,?6.,97 

?*h 

?6.74 

87.3 

*4fl8 

02.67 

W3 

?4.9 

42.61 

84,? 

69.79 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


17 


|4? 

15° 

/ 

T 

E 

c 

M 

X 

Y 

T 

£ 

C 

M 

y 

Y 

7O3.5I 

43.03 

1396.5 

42.7/ 

I386./ 

\7O2P 

7f4.32 

49.44 

)49S7 

49.02 

1482.9 

I9f.23 

O 

04.36 

43.13 

90.Z 

42.81 

877 

70.60 

SS.'7 

49.55 

97.4 

49.  13 

#4.6 

95:66 

1 

Of.ZO 

43.24 

99.8 

4291 

99.4 

71.oo 

56.02. 

49.66 

99.0 

49.24 

06.2 

96.  lo 

2 

06.05 

43.34 

1401.5 

43.0  / 

91  o 

7/.4I 

S6.97 

49.77 

1500.7 

49.34 

979 

96.53 

3 

0690 

4*44 

03.2 

43.12. 

92.6 

7/.8I 

S7.7/ 

49.88 

02.3 

49.45 

89.4 

96.96 

4 

07.74 

A3.  55 

04.8 

43.2Z 

94.Z 

72.22 

5&S(, 

So.oo 

04.0 

49.56 

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97.40 

5 

08  S  ~9 

43.65 

06.5 

43.32 

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72.62 

5-9.41 

SO.  II 

057 

49.67 

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97.83 

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09.4-3 

43.75 

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4)42 

97.4 

73.03 

60.26 

So  ZZ 

07.3 

49.78 

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98.26 

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to.i* 

43.86 

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73.44 

61.11 

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98.70 

8 

11.13 

43.96 

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43.63 

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73.94 

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50.00 

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44.07 

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174.25 

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44.17 

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63.65 

So  67 

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50.22 

15-006 

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// 

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4427 

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75:07 

64.50 

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So.33 

02.3 

00.44 

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14.5-1 

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44.04 

07.  f 

7JI48 

65.35 

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17.Z 

50.44- 

03.9 

00.88 

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'$-.36 

44.48 

19.7 

44.14 

08.8 

7S.89 

66.20 

5/.00 

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50.55 

05.5 

0/32 

14 

16.  20 

44.?9 

21.3 

44.24 

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76.30 

67O4 

s/n 

ZO.S 

&.(>(, 

07.  / 

01.76 

fS 

17.0  f 

4469 

£3  o 

44.35 

I2.o 

76.71 

67.99 

S/.23 

22.2 

S0.77 

Og.7 

02.19 

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17  90 

44".  80 

24.7 

44.4-5 

13.6 

77.12. 

68.74 

S'M 

23.8 

S0.88 

/0.3 

02.63 

17 

'9.74 

44.90 

26.3 

44.56 

15.2. 

77.53 

69.59 

S'.*S 

25.? 

f/.OO 

If.  9 

03.07 

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f9.59 

45.  o; 

28.o 

44.66 

I6.B 

7/94 

70.44 

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27.1 

f/./> 

13.5 

03.51 

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72O.44 

45.12 

J4£9.6 

44.76 

14184 

170.35 

77/.Z9 

S/.(,8 

15-28.8 

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/&5.I 

2.03.95 

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21,28 

4-5:22 

31.3 

4427 

20.  \ 

79.77 

72.13 

51.79 

30.4 

51.33 

X6-.7 

04.39 

21 

22.  13 

4S.33 

32.9 

4497 

21.7 

79.18 

72.98 

fl.9t 

32.1 

S/.44 

/8.3 

04.84 

22 

22.98 

45.43 

34-6 

45.08 

23.3 

79.59 

73.^3 

52.02 

33.7 

S/.SS 

19.9 

OS.18 

23 

23  82 

45.54 

362 

45.  18 

24.9 

SO.oi 

74.68 

52.13 

35.4 

S/.66 

ZI.5 

05.72 

24 

£4.67 

45.65 

37.9 

4S.2S 

265 

8042 

Tf.53 

52.25 

37-0 

S/.77 

23.2 

06.  /6 

25 

25.52 

4S.7S 

39.5- 

45.39 

23.  / 

80.84 

7638 

52.36 

38.7 

S/.89 

24.8 

06.61 

26 

2636 

45.£6 

41.2 

4S49 

29.7 

81-25 

77.23 

52.47 

4o.3 

SZ.oo 

264 

07.05 

27 

2.7.21 

45.96 

42$ 

45.60 

31.4 

81.67 

78.07 

5259 

42.o 

52.11 

£80 

07.49 

28 

2?.  06 

46.07 

44.5 

4S.70 

33.0 

82.09 

78.9  a 

52.70 

43.6 

52.22 

29.6 

07.94 

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723.90 

46.18 

14462 

45.91 

1434  .6 

18250 

779.77 

,52.82 

1545.3 

5234 

Ittl.Z 

208.38 

30 

29.75 

46.2? 

478 

45.91 

36.2 

82.92 

80.62. 

52.93 

469 

52.45 

323 

09S3 

31 

30.60 

46.39 

49.  f 

46  02 

37.8 

83.34 

21.47 

53.05 

48.6 

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34.4 

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46.50 

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39.4 

31.76 

9232 

53.16 

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52.67 

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46.23 

4-1  O 

84.18 

83.17 

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52.79 

37.6 

10.17 

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33.  /4 

46.71 

54.4 

46.34 

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84.60 

84  02 

5339 

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52.90 

39.  2 

I0.6Z 

35 

33.99 

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56.1 

4644 

44.3 

85.02 

84.96 

53.51 

55.2 

S3.0\ 

40.8 

11.07 

36> 

34.33 

46.93 

577 

46.55 

45.9 

8544 

85.7/ 

5*6? 

56.9 

53.12 

42.4 

)L5I 

37 

35.6? 

47.04 

59.4 

46.6? 

47  S 

85.96 

86.56 

53.74 

58.5 

53.24 

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30 

3653 

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46.76 

49.1 

86.28 

£74/ 

53.95 

60.? 

33.35 

45.6 

12.41 

39 

73737 

47.25 

1462.7 

44.87 

14*0.7 

18670 

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5337 

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S3.46 

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2/2.86 

40 

38.22 

47.36 

64-? 

46.97 

52.3 

87.12 

89.11 

54.08 

63.5 

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48.8 

13.31 

41 

39.07 

4747 

66.0 

47*0 

53.9 

87.54 

89.96 

54.  *0 

65.1 

53.69 

50.4- 

13.76 

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47.5* 

67.6 

47/9 

55.6 

87.97 

90.91 

54.  32. 

66.9 

S3.SI 

&] 

I4.ZI 

43 

40.76 

47.69 

69.3 

4729 

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08.33 

97.66 

54.4-3 

68.4 

53.92 

5-J.7 

X4.67 

44 

4-1.61 

4780 

70.9 

47.40 

58$ 

98.92 

92.5"' 

54.55 

70.1 

54.03 

5^3 

IS.  IZ 

45 

42.46 

47  #> 

72.6 

47.51 

60.4 

89.24 

93.3€ 

5-4.67 

7t.7 

54  .15 

£6\9 

I5-.S7 

46 

43.?o 

48.01 

743 

47.61 

620 

89.67 

94.ZI 

5478 

73.4 

5-4.26 

5R5 

16.02 

47 

44.  >5 

42.12. 

7f.9 

4-7.72 

63.6 

90.09 

9J-.05 

54.90 

75-.0 

54.3* 

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16.49 

48 

45.00 

48.23 

776 

47.83 

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70.52 

95.90 

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~%.7 

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745.F5- 

48.34 

1479.2. 

47.94 

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190.9^ 

796.75" 

&.I3 

1578.3 

54f>\ 

15633 

2/7.39 

fO 

46.69 

48.45 

80.9 

48.04 

68A 

9137 

97.60 

55.ZS 

80.0 

54.72. 

64.9 

17.24- 

51 

47.54 

48.56 

82.5 

48.  IS 

70.1 

91.80 

9*.*$- 

55.37 

8t.G 

54X4 

66.5 

18.30 

52 

49.39 

48.67 

84.2 

48.26 

71.7 

92.23 

39.30 

5S148 

83.3 

5495 

68.1 

I8.7S 

S3 

4-9Z4 

48.78 

85.8 

48.37 

73.3 

92.65 

800./5 

55.60 

84.9 

55.07 

69.7 

V.2I 

54 

So.08 

48.81 

37.S 

49*8 

749 

93.08 

OI.OO 

55.72 

86.6 

5S.I8 

71.3 

/9.67 

55 

So  93 

49.00 

99.1 

48.58 

76.5 

93.51 

01.  SS 

55.94 

98.2 

55.30 

72.9 

20.12. 

5-6 

5/.7* 

4^11 

90.8 

4*69 

7g.l 

93.94 

02.70 

55.9S 

89.9 

SS.4I 

74.5" 

20.5-8 

S7 

52.63 

4922 

92.4 

48.80 

79.7 

9437 

03.55 

56.07 

9/.5 

55.53 

Tf.t 

21.04 

5S 

53.48 

49.33 

941 

48.91 

9  1.3 

94.80 

04.40 

56.19 

932 

55.64 

77.7 

21.  SO 

59 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


, 

16° 

\r 

T 

E 

C 

M 

X 

Y 

T 

E 

C 

M 

X 

Y 

0 

805.25 

56.31 

1594.8 

J5.76 

I57S>3 

2Z/.96 

856  3O 

63.63 

163J.S 

62  94 

16/5"  2 

25036 

/ 

06.  10 

56.43 

96.5 

55.88 

80.9 

57.15 

63.76 

95.4 

6*06 

76.8 

$0.85 

2 

0&  QB 

S6.5S 

98.1 

55.93 

815 

22.89 

58.01 

63.89 

97.1 

63.  18 

78.4 

513} 

3 

07.90 

56.66 

56.11 

84.1 

^3.34 

58.86 

6401 

98.7 

63.31 

Boo 

51.  81 

4 

08.65 

56.  7g 

1601.4 

S6.Z3 

85.7 

23.90 

5971 

64.1  A 

1700.4 

63.43 

8/6 

S2.3I 

5 

09.50 

56.90 

03.1 

56.34 

87? 

24.26 

.  60.56 

64.27 

02.0 

63.55 

83.2 

fl.80 

6 

10.  35 

57.02 

04.7 

S6.4(, 

98.9 

24.7<? 

61.41 

64.39 

03.7 

63.68 

84.7 

53.23 

7 

II.  ZO 

57.14 

06.4 

56.58 

90S 

15.  18 

6Z.Z7 

64.52 

05.3 

(J.80 

S6.3 

53.78 

8 

m.or 

f7i6 

08.0 

56.69 

92.1 

25.65 

63.12 

6465 

07.0 

63.92 

87.9 

54.27 

9 

12.30 

5-7.38 

09.7 

S6.8I 

93.7 

26.11 

63.97 

64.77 

08.6 

64.05 

99.5 

54.76 

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8I3.7T 

57.50 

16  H.  3 

56.33 

1  r95.  3 

22657 

564.82 

64.90 

17/0.2 

64\/7 

I(>3I  1 

255-.2S 

II 

14.60 

5762 

13.0 

S7.04 

96.9 

27.04 

65.68 

65.03 

11.9 

64.30 

32.7 

55.75 

IZ. 

I5.4f 

57.74 

I4A 

9».5 

27-50 

66.53 

65.15 

13  (, 

64.4Z 

94.3 

56.Z4 

13 

16.30 

57.96 

16.3 

S7.23 

\6oo.l 

27.97 

£^38 

&  5"  2.% 

15.  2 

64.55 

95.3 

56.73 

14 

17.15- 

57.98 

17.3 

S7.40 

01.7 

2843 

68.23 

65.41 

/69 

64.67 

97.5 

5723 

15 

18.00 

19.6 

57.51 

OJ.3 

28.90 

69.09 

65.54 

/8.5 

6400 

99.1 

57.72 

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19.95 

58.22 

2/.2 

57.6) 

04.9 

29.37 

69.94 

65.67 

20.? 

64.92 

I7O0.7 

Sg.ZI 

/7 

13.70 

5834 

22.9 

S7.75 

06.5 

29  93 

70.73 

65.79 

21.9 

65.05 

02.3 

/8 

2o.F5 

59.46 

24.S 

57.37 

08.1 

3030 

7/.64 

65.92 

2*5 

65.17 

03.9 

f9.ZO 

/9 

2/.4o 

58.58 

26.2. 

S7-99 

09.7 

30.77 

7f.5o 

66.05 

2.5-.I 

65.30 

S9..70 

20 

8ZZ.25 

50.70 

;62.78 

50.10 

161  1.3 

Z3I.24 

97J.3F 

66.  18 

1726.8 

6£42 

1707.0 

260.20 

2  1 

23.  10 

58.92 

29.5 

58.22 

/2  3 

31.71 

74.20 

66.31 

28.4 

65.5-j 

08k 

60.69 

ez 

Z3.9S 

SB.  94 

31.1 

58.34 

H's 

32.18 

75.05 

66.44 

30.0 

65.67 

61.  19 

23 

2*J  QO 

59.06 

32-8 

58.46 

16.1 

32.65 

7*9  1 

6.6.56 

31.7 

65.80 

U'-9 

61.69 

£4 

££66 

59.19 

34.4 

17.7 

33.  12 

76.76 

6669 

33.3 

65.  93 

13.4 

t>2.\3 

25 

26.5-7 

59.31 

36.1 

57.70 

19.3 

33.59 

77.6  \ 

66.82 

35.0 

66.05 

15.0 

62.69 

£G 

27.36 

59.43 

37.7 

53.82 

20.9 

34.06 

78.47 

66.95 

66./g 

/6.6 

*>*.)% 

27 

22.ZI 

59.  5  f 

33.4 

22.5 

34.53 

79.32 

67.08 

38.3 

66.30 

19.2 

63.68 

29 

29.06 

5967 

4l.o 

5*9.06 

24-  / 

35.00 

80.17 

67.21 

39.3 

66.4J 

19-9 

64.18 

29 

59.79 

4Z.7 

59.  n 

257 

35.48 

81.02 

6734 

4/6 

66.56 

2.1.3 

64.68 

3o 

830.76 

S9.9I 

1644.3 

.59.29 

16273 

235.95 

891.88 

67.47 

1743.2 

66  6g 

17223 

265.19 

31 

3/.6I 

€>o  04 

46.0 

59.41 

28.9 

36.42 

82.73 

67.60 

44.3 

66'.gl 

24.5 

65.69 

32 

3246 

60.16 

47.6 

59.53 

30  f 

36.90 

83.58 

67.73 

46.5 

66.94 

Zf>.\ 

66.19 

33 

3J.3/ 

60.28 

4-9.3 

5*65 

3SJ 

3737 

84.44 

67.86 

48.2 

6707 

27.7 

6669 

314 

3A./6 

60.40 

F09 

S9.77 

33.7 

3795 

85.29 

67*9 

49.8 

67(9 

2.9-3 

67/9 

315 

J!5"  01 

fyC   5*3 

52.6 

35.3 

38.32 

86.14 

68.12 

51.5 

£7  ?2 

30.9 

6770 

36 

35-87 

60  '65 

54-2 

60.01 

36.9 

58.80 

#700 

68.25 

53.1 

6745 

32.5 

68.20 

37 

36.7* 

60.77 

SS9 

60.17 

38.5 

39.27 

87.8S 

€8.38 

548 

67.57 

34.1 

6871 

39 

37-57 

60.99 

60.  zs 

4o.l 

39.75" 

88.70 

68.51 

564 

67.70 

35.7 

69.21 

39 

38.41 

6  (.02 

59SZ 

60.38 

41.7 

40.23 

99.  5  6 

68.64 

58.1 

6793 

372 

69.71 

40 

839.27 

61.14 

1660.9 

60.50 

1643.3 

240  71 

990.41 

68.77 

1759.7 

67.96 

1738.9 

Z70.ZI 

41 

4o.lZ 

£/-2& 

61.5 

60.6Z 

44.9 

41.19 

91.2k 

6891 

61.3 

68.09 

4o.4 

70.73 

AZ 

40.97 

61.39 

64.1 

60.74 

46.5 

4-1.66 

92.12 

69.04 

63.0 

68.21 

Atp 

43 

4/.|J 

61.51 

65.8 

60.96 

4-8J 

42.14 

92.97 

69.17 

64.6 

6£J4 

43.6 

71.74 

44 

£/  64 

674 

60.98 

49.7 

42.6Z 

9J.82 

f>9  3o 

66.3 

68.47 

45.  Z 

72.25 

45 

43'.53 

6l'.76 

69.  1 

61.10 

51.3 

43.10 

94.68 

69.43 

679 

68.60 

46.8 

72.76 

46 

44.38 

61.98 

70.7 

6I.ZZ 

52.9 

43.5? 

95.53 

69.56 

69.6 

68.73 

48.4 

7j  26 

47 

4S.2.3 

62.01 

72.4 

61.34 

54.5 

44.06 

96.39 

69.69 

71.2 

68.86 

49.9 

7J.77 

48 

46-08 

6Z.I3 

74.0 

61.47 

56  1 

44.54 

97.24 

6983 

72.9 

68.99 

SI.  5 

74.28 

49 

46.93 

62.26 

75:7 

61.59 

S7.6 

4-5.03 

98.09 

69.96 

74.5 

69.11 

53.1 

7479 

So 

847.78 

62.38 

1677.3 

61.71 

1659.2. 

245.  51 

898.95 

70.09 

177*.  2 

69.24 

I7F47 

2753o 

51 

4%  64 

62-5' 

79.0 

61.81 

60.8 

45.99 

99.80 

70.  21 

778 

69.37 

56.3 

7$  "81 

52 

49.'49 

61.95 

62.4 

46.48 

900.65 

7036 

79.5 

69.50 

57.9 

7*32 

53 

fO.34 

6Z76 

82.3 

62.08 

64.0 

OI.5/ 

70.49 

91.1 

69.63 

59.5 

7^.84 

54 

5V.  /9 

6z.es 

93.3 

62.20 

65.6 

47.44 

02.36 

70.62 

82.8 

69.76 

61.0 

77.35 

55 

52.04- 

63.01 

85.5 

62.32 

67.2. 

47.93 

03.2Z 

70.75- 

844 

69.89 

62.6 

77.96 

56 

S2.99 

63.13 

6244 

68.8 

48.4-1 

04.07 

a?.89 

86.0 

70.ot 

64.2 

76.37 

57 

53.75 

63.26 

99% 

62.57 

70.4 

49.90 

04.92 

71.01 

877 

70.15 

65.9 

78.89 

58 

S4.60 

63.30 

49.38 

05.78 

7A/5 

85.3 

7o  28 

674 

79.40 

5"9 

63.51 

9Z.I 

62.8' 

74.6 

49.97 

O6.63 

7/.29 

91.0 

/fc4l 

69.0 

79.91 

UNIVERSH 


TAB! 


^FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


18° 

19° 

/ 

T 

E 

c 

M 

X 

V 

T 

E 

C 

M 

X 

Y 

907.49 

71.41 

I792.& 

70.S4 

n?o.(= 

290.43 

9S8.BI 

7967 

1891.3 

78.58 

J565.4 

312.16 

O 

08.34 

7/.5S 

94.3 

70.67 

72.1 

80.94 

59.67 

79.81 

930 

7872 

67.o 

12.70 

» 

O9.2O 

7/.69 

95:9 

70.80 

73.7 

81.46 

60.*] 

79.95 

94.6 

7835 

68.  S 

13.25 

2 

lo.os 

7/.S2 

976 

709) 

7Z.3 

81.98 

61.38 

90.)  '0 

963 

78.99 

70.1 

13.79 

3 

IO.9O 

7/% 

99.  2 

7/.06 

76.9 

8Z.49 

6f.Zt- 

$014 

97.9 

79.13 

71.7 

14.31 

4 

11.76 

72.03 

800.9 

7/./9 

78.  5 

83  .01 

6i.lo 

8o.)9 

995 

79.  Z7 

73.3 

/4.98 

5 

12.61 

72.22 

02.5 

7/.J* 

$0.1 

83.53 

63.96 

80.52 

1901.  2 

79.41 

748 

15.42 

6 

13.47 

72.X, 

04.2 

7'Af, 

91.7 

84.05 

6431 

90.66 

028 

79.54 

76.4 

IS  97 

7 

14.31 

72.4") 

05.8 

7/5"? 

m 

84.57 

65.67 

BO.BI 

04.5 

79.68 

78.0 

16.51 

8 

15.18 

72.63 

07.4 

7/72 

84.8 

85.08 

66.53 

go.95 

06.1 

79.8Z 

79.6 

17.06 

9 

91603 

72.76 

S09.I 

7/.£r 

78(>4 

285.60 

967.38 

g/.09 

1907.8 

7996 

1891.  1 

3>7.6I 

/o 

16.89 

72.90 

10.7 

7/98 

8B.O 

86./2 

68.24 

8/.23 

094 

80.10 

827 

/8.I6 

// 

17.74 

73.03 

12.4- 

72.11 

89.6 

»6.64 

69.  to 

61.38 

If-/ 

8o.l4 

84.3 

18.70 

12 

18.60 

73.17 

I4.o 

72.25 

91.2 

87.16 

69.96 

$1.52 

12.7 

$0.3% 

85.9 

19.25 

13 

19.4-5 

73.30 

IS.  7 

72.38 

92.7 

87.69 

70.91 

S/.66 

143 

80.52 

87.4 

19.90 

14 

20.31 

7344 

17.3 

72.51 

943 

88.21 

71.67 

81.81 

16.0 

#0.66 

89.0 

20.35 

15 

21.  It 

7J.S8 

19.0 

72.64 

959 

88.73 

7Z.S3 

8f.9S 

17.6 

00.79 

90.6 

Z0.90 

Ik 

22  02 

73.71 

20.6 

72.78 

97.5 

e9.2S 

73.38 

82.09 

19.1 

S0.13 

92.2 

21.45 

n 

22.87 

73.25 

22.3 

72  9/ 

99.1 

8977 

74.24 

82.2* 

20.9 

21.07 

93.7 

22.00 

19 

23.73 

73:98 

23.9 

7J.04 

BOO.G 

90.30 

75.  10 

02.38 

22.6 

21.  21 

9X3 

2155 

/9 

924.58 

74.it 

;825.6 

73.  /  7 

802  a 

23o$2 

97*96 

82.53 

/924Z 

8/.3f 

8969 

323.10 

20 

25.44 

74.26 

27Z 

73.  31 

03.8 

97.35" 

76.91 

9t.er 

25J8 

8149 

98.5 

23.66 

21 

26.29 

7*39 

28.8 

73.44- 

05.4 

91.27 

77.67 

82.21 

17.5 

81.63 

9oo.o 

24.21 

2t 

27.  15 

7*53 

305 

7357 

07.  0 

92.40 

7853 

82.96 

29.1 

21.77 

01.6 

24.76 

23 

29.00 

74.67 

32.1 

73.70 

08.6 

92.92 

79.39 

8J.IO 

30.g 

81.91 

03.1 

25.31 

24 

28.86 

7480 

33.8 

7*84 

10.1 

93.45 

SO  24 

83.25 

32.4 

82.05 

04.7 

25.87 

25 

-29.7/ 

7494 

35.4- 

73.97 

11.7 

93.98 

8/./0 

83.39 

34.1 

82.20 

06.3 

26.42 

26 

3057 

Tf.08 

37.1 

74.11 

13.3 

94.  fo 

81.96 

83.54 

35.7 

82.34 

079 

26.98 

27 

3/.4Z 

Tf.21 

38.7 

74.24 

14.9 

95.03 

8E.«2 

83.62 

37? 

82.48 

09.5 

"27.53 

28 

32.28 

7S.35 

4o.4 

74.37 

/6.S 

95.  S6 

83.68 

83.83 

39.0 

8Z.62 

ll.o 

28.09 

29 

933.13 

7*49 

1842.0 

74.51 

J8/8.0 

296.09 

984.53 

83.97 

/94o.fc 

32.76 

J9J2.6 

318.64 

30 

33.39 

7#-63 

43.6 

74.64 

19.6 

96.61 

85.39 

84.12. 

42-3 

82.90 

14.2 

29.20 

31 

54.84 

7f.76 

45.3 

74.77 

21.2 

97.15 

86.25 

84.26 

43.9 

83.04- 

15.7 

29.76 

32 

35.70 

7X90 

4&9 

74.91 

22.3 

97.68 

87.  II 

84.V 

45.6 

B3.IS 

17? 

30.32 

33 

36.55 

76.04 

4-3.G 

7JT.04 

Z4.4 

98.21 

97.97 

84.  5T 

472 

$3.32 

18.7 

30.87 

34- 

37.41 

76.18 

50.2 

75  19 

2  £9 

99.74- 

$832 

94.70 

4-8.9 

8347 

20.S 

31.43 

35 

38.27 

76.32 

SO 

75.31 

27.5 

99.27 

89.68 

34.85 

50.5 

83.  61 

22p 

31.99 

36 

39./Z 

76.45 

53.5 

75.45 

29.  / 

99.90 

90.54 

9499 

52..  1 

33.75 

236 

32.55 

37 

39.98 
4o.93 

7659 
76.73 

55.2 
56.8 

75.58 
75.72 

30.7 
32.3 

300.33 
00.87 

9/.40 
92.26 

85.14 
95.28 

53.9 
S5.4. 

33.99 
94.03 

25T.2 
26.7 

33-H 
33.67 

38 
39 

941.69 

76.37 

IS58.4 

7f.3S 

/833.S 

301.40 

993.  K 

85.43 

I9f7./ 

84.1S 

1928.3 

334.23 

4-0 

42.55 

77.oi 

60.1 

7f99 

35.4 

OI.93 

93.37 

85.58 

59.7 

84.32 

29.9 

34.79 

41 

43.40 

77.15 

(,1.7 

76.lt 

370 

02.47 

34%3 

85.72 

60.3 

S4.4S 

3/.4 

35J5 

4-t 

4426 

77.29 

63.4 

76.26 

3B.(, 

03.00 

95.69 

S5.87 

62.0 

94.60 

33.0 

35.  9? 

43 

4-5.11 

77.43 

65.0 

76.39 

40.Z 

03.54 

9&S5 

86.02 

63.6 

84.7S 

34.6 

36.49 

44 

45.97 

7757 

66.7 

76.53 

41.7 

04.07 

97.4; 

V6J7 

6f.3 

84.89 

367 

37.04 

45 

46.83 

77.70 

69.3 

76.66 

43.3 

04.61 

98.27 

96.31 

66.9 

85.03 

377 

3760 

46 

47.68 

77.94 

70.O 

763,0 

443 

05.14 

99.  13 

86.46 

68-5 

«f.|8 

39.3 

38.17 

47 

48.54 

77.98 

7L6 

76.94. 

46.5 

05.68 

99.98 

86.61 

70.Z 

8S.32 

40.9 

38.73 

M 

43.  39 

Tg.lZ 

73.2 

77.07 

4*0 

06.22 

1000.8 

86.76 

7t.3 

85.46 

42.4 

39.30 

49 

950.25 

78.26 

1*743 

77.21 

1849.6 

306.76 

IOOI.7 

86.90 

1973.5 

85.61 

J944.0 

339.86 

so 

5/.M 

78.40 

76.5 

77  35 

5U 

0729 

02.6 

0705 

7F.I 

9£7S 

455 

40.43 

51 

SI  96 

78.54 

78* 

77.49 

52.8 

07.8? 

03.4 

87.20 

768 

85.89 

4.7.1 

A039 

52 

52.82 

70.62 

79.9 

77.  61 

54.4 

08.37 

04.3 

8735 

78.4 

86.04 

48.7 

41.56, 

« 

5*68 

78  8? 

81.5 

77.  76 

5J.9 

08.9/ 

05.1 

3750 

Bo.o 

96.18 

50.3 

42.13 

54 

Jaw 

78.97 

83.1 

77.99 

575 

09.45" 

06.0 

8764 

81.7 

86.32 

51.8 

42.70 

SS 

SS.39 

79.11 

84.9 

79.03 

59.  / 

09.99 

06.9 

8779 

93.3 

et.47 

5*4 

43.26 

.56 

5624 

79.25 

86.4 

78.\7 

60.7 

/0.53 

07.7 

8794 

850 

96.61 

55.0 

43.83 

5? 

57/o 

79.39 

88.0 

79.30 

62.2 

11.07 

08.6 

88.09 

866 

86.76 

56.5 

44.4o 

58 

57.9fe 

79.53 

89.7 

•78.44 

63.8 

II.6Z 

09.4 

88.24 

8V.Z 

869o 

58.1 

44.97 

59 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

£0° 

21° 

T 

E 

c 

M 

X 

Y 

T 

E 

C 

M 

X 

Y 

0 

10/0.3 

8339 

19893 

"B7.0F 

1959.7 

34554 

IO6/.9 

9752? 

20883 

95.94 

£053.3 

3gQ56 

/ 

11.2 

8854 

9/5 

S7./9 

6/.Z 

46.  // 

62.9 

977/ 

89.9 

96./<? 

54.9 

8/./6 

z 

12.0 

80.69 

93.2 

97.34 

613 

4£.l£ 

63.7 

9789 

91.6 

9^.25 

56.4 

81.76 

3 

IZ.9 

8884 

94.8 

87.48 

64.4 

4725 

64.5 

98.CS 

93Z 

96.40 

5?.o 

£2.35 

4 

13.1 

88.99 

965 

87.63 

659 

4X82 

65.4 

98.21 

94g 

96.55 

59.5 

kar 

S 

I4& 

89J4. 

99.1 

97.77 

67  S 

48.40 

66.2 

90.36 

96.5 

96.70 

61.1 

8355 

6 

/S.4- 

89.19 

99.7 

8792 

69.1 

49.97 

67/ 

98.52 

99.1 

96.86 

62.7 

84& 

7 

/(>.3 

59.44 

^OOI.4 

88.06 

70.6 

49.5  A 

68.0 

W68 

99.8 

97.01 

64.2 

94.75 

S 

17.  2 

89.59 

O3.o 

99  Zl 

722 

50.12 

688 

98.84 

Z\o\A 

97/6 

65.8 

85.X 

9 

I8P 

8974 

04.7 

98.35 

73.7 

50.69 

69.7 

990) 

03.0 

97.32 

673 

85.95 

IO 

1018.9 

89.89 

2oo63 

SSSo 

'97S3 

3?/.£6 

J070.6 

99.15 

2/04.7 

97.47 

2068.9 

386.56 

11 

197 

90.04 

07.9 

88.15 

76.9 

51.84 

7/4 

9931 

06.3 

9762 

704 

87.16 

IZ 

206 

9o.l9 

09.6 

88.79 

7g.4- 

5241 

72.3 

95.47 

O8.o 

9777 

72.0 

87.76 

/) 

21.5 

9o.H 

11.2 

88.94 

?0.o 

5239 

73.  / 

99.63 

09.6" 

979? 

73.5 

88.36 

it- 

223 

90.49 

12.9 

89.08 

g/.6 

53.57 

74P 

99.79 

11.2. 

9*08 

7SJ 

88.97 

is- 

Z3-2 

9o.64 

14.  S 

89.23 

83./ 

54.14 

74.9 

99.95 

72.9 

98.2? 

76.6 

$9.57 

/6 

24.0 

9079 

16.1 

?93g 

?4.7 

54.72 

7J7 

100.11 

74*5" 

98.39 

78.2 

90.  1? 

17 

24.9 

9o.94 

178 

89.52 

96.3 

55.30 

76.6 

00.17 

/6.7 

9?54 

79.7 

90.78 

J8 

25.8 

91.10 

/9.4 

99.67 

S78 

5587 

77.  S 

00.43 

/7.g 

9S70 

81.3 

9/38 

/9 

26.6 

91.  ZS 

2/.I 

99.92. 

89.4 

ft.4y 

70.3 

00.59 

19.4 

5>8.'8S 

82.9 

97.99 

ZO 

IOZ7.S 

91.40 

2022.7 

89.96 

1990.9 

357.03 

/079.Z 

I00.7S 

2121.  1 

99.00 

2084.4 

392.60 

it 

28.3 

9I.SS 

24.3 

90.11 

92.S 

57.61 

SO.o 

00.91 

22.7 

991k 

86.0 

93.20 

2Z 

29.2 

91.70 

26.0 

90.26 

94.1 

S8.\9 

80.9 

01.07 

*4.3 

99.31 

87.5 

93.87 

£3 

30.1 

91.86 

£76 

90.41 

95.6 

58.77 

81.8 

0/.23 

26.0 

9947 

99.  1 

94.42 

24 

J0.9 

92.01 

29.5 

9o.  SS 

97.Z 

59.  JF 

82.6 

0/.39 

276 

99.6Z 

90.6 

9f.03 

25 

3l.g 

92.16 

J0.9 

9070 

388 

539 

83.5 

0/.55 

29.2 

99.78 

92.2 

95.63 

26 

32.6 

92.31 

32.5 

90.85 

2000.3 

60.  S 

£4.4- 

0171 

30.9 

99.93 

93.7 

76.24 

27 

33.5 

93.47 

34.2. 

91.00 

0/.9 

61.10 

85.2 

01.  S  7 

32.5 

JOO.O9 

95.3 

96.85 

29 

34.4 

92.62 

35.8 

91.14 

03.4 

6I&8 

86.  \ 

02.03 

34-2 

O0.24 

96.8 

9746 

29 

3« 

92.77 

375 

91.29 

05.0 

62.26 

f(>.9 

02.J9 

353 

0040 

98.4 

98.07 

3& 

/036.I 

#.92 

2039.  » 

9/.44 

2006.6 

362.85 

1097.9 

/02.35 

27374 

/00.SS 

20999 

398.68 

3/ 

370 

93.08 

40.7 

9/.S9 

OS.I 

63.43 

88.7 

02.51 

39.1 

00.11 

ZIOI.  5 

99.29 

3i 

37« 

93.23 

4z* 

9A74 

09.7 

64.0/ 

89.  5 

0267 

4o.-7 

00.86 

03.0 

9991 

33 

38.7 

93.38 

44.0 

9/.89 

n.z 

64.60 

90.4 

02>3 

42.3 

0/.02 

04.6 

400.52 

34 

335 

93.54 

4F.7 

9204 

72.8 

65.  /8 

913 

02.99 

44.0 

01.18 

06.1 

01.13 

35 

4o.4 

93.69 

47.3 

92  (8 

/4.4 

65.77 

92.1 

03.16 

45.6 

01.33 

077 

01.74 

36 

41.3 

93.85 

48.9 

9Z.33 

'f.9 

6636 

93.0 

0332 

473 

O/.49 

09.Z 

02.36 

37 

42.1 

94-.oo 

506 

92.48 

'7.  S 

6694 

93.9 

<?3.48 

48.9 

07.64 

10.8 

0297 

38 

41o 

94.1  '5 

52.Z 

9263 

/9.0 

67.53 

94.7 

03.64 

.50.5 

01.30 

12.3 

03.58 

39 

43.8 

94.31 

5/.9 

a?.?* 

2o.6 

68.  /2 

95£ 

O3.?0 

^2.2 

07.96 

U.<) 

04  20 

40 

/044.7 

94.46 

2oyj-y 

92.93 

20Z2.Z 

368  7/ 

/096.4 

/03.97 

2/53.8 

/02./  1 

2775.4 

404.8/ 

41 

45.6 

94.62 

S7.I 

93.08 

23.7 

69.29 

973 

0413 

J54 

02.Z7 

17.0 

05.43 

42 

444 

94.77 

58.8 

93  Zl 

25.3 

69.8g 

98.2 

04.29 

57./ 

0243 

185 

Ot.05 

43 

4-7.3 

94.93 

60.4 

93.38 

Z6.8 

7047 

99.0 

^4.45 

58.7 

02.5? 

20.1 

06.66 

44 

48.1 

95.08 

62.1 

SB.53 

ZV.4 

7/.06 

99.9 

^4.62 

60.4 

02.74 

2(6 

07.28 

4f 

4*0 

95:24 

63.7 

9J.68 

30.0 

7/65 

/  100.8 

04.78 

62.0 

OZ.90 

23.2 

07.90 

46 

49.9 

95.39 

65.3 

9^.?3 

3;.r 

72  a4 

01.6 

04.94 

63.6 

03j%, 

Z47 

08.SI 

47 

5*>.7 

9ST.W 

67.0 

W.98 

33.  \ 

72.83 

02.5 

OS.\\ 

65!3 

03  .21 

26.3 

09.  J  3 

4€ 

5/.6 

95:70 

6g£ 

94.13 

34.6 

73.43 

03.4 

05.27 

669 

03.37 

27.8 

0975 

44 

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ar.86 

7»* 

94.29 

36.t 

74.02 

04.2 

05.43 

eg.f 

03.53 

29.4 

10.37 

SO 

7053.3 

96.0| 

207/.9 

14.41 

20378 

374.6  ( 

»05.  1 

/<?5.60 

•ZI70Z 

703-69 

2730.9 

4/0.99 

fl 

54.2 

56.17 

7*5 

94.58 

393 

7flo 

05.9 

05.76 

7/9 

03.84 

324 

11.61 

SZ 

*5.o 

96.3? 

7S.Z 

94.73 

40.9 

7f.9o 

06.8 

05.92 

7^.4- 

04.00 

34.0 

12.23 

S? 

55.9 

96.4S 

768 

94.28 

42.4 

76.39 

077 

06-09 

7  S.I 

04.16 

35? 

12.95 

54 

569 

96£4 

78.S 

95.03 

44.0 

7638 

08.5 

06.25 

76.7 

04.12 

37  / 

13.47 

SS 

576 

9K.79 

go.  1 

95:/9 

45.5 

77.58 

09.4 

06.42 

7*4- 

<*4g 

3?.6 

14.10 

S6 

58.5 

96.95 

8/.7 

95:34 

47.  / 

78.19 

tO.3 

06.58 

9o.o 

0463 

4o.z 

/47? 

57 

59.3 

97.11 

8J.4 

95.49 

4*7 

78.77 

ll.l 

06.7T 

81.6 

0479 

41.7 

15.34 

S8 

60.2 

97.26 

8fO 

95.6* 

5V7.Z 

7937 

120 

06.9  f 

B3.3 

04.95 

43.3 

15.96 

W 

61.  f 

97.4-2 

967 

9579 

f/.g 

79.96 

12.9 

07.08 

84.9 

05J/ 

44.8 

/6.S9 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


2L 


22° 

25° 

, 

T 

E 

C 

M 

X 

Y 

T 

E 

C 

M 

X 

Y 

'"3.7 

IO7z4 

2186.5 

/Of.2.7 

2/46.4- 

4-17.21 

1165.7 

117.38 

2294.6 

//S&2. 

2Z3R8 

455.48 

o 

/4.6 

07.41 

88.Z 

05.4-1 

479 

17.83 

66.6 

17.55 

36  2 

/$  }*$ 

403 

56.;  3 

1 

15.5 

07.57 

89.8 

0559 

49.5 

1846 

674 

17.73 

879 

1536 

AlS 

2 

0774- 

91.4 

/9.09 

6*3 

17.90 

89.5 

43.4 

5743 

3 

I7.Z 

07.90 

93.} 

05.  9  1 

5-2.5 

19.71 

69.  Z 

18.07 

91.1 

15.69 

44.9 

S8.09 

4 

12.1 

08.07 

94.7 

06.07 

54.  / 

3>.34 

70.1 

18.25 

92.2 

/5.96 

464 

5874 

5 

/$*) 

09.23 

96.4 

06.23 

556 

20.97 

70.9 

1842 

94.4 

16.01. 

490 

59.39 

6 

/s'g 

0844 

98.0 

06.39 

S7Z. 

21.59 

7/.g 

18.60 

96.0 

/b.\9 

49S 

6005 

7 

20.7 

02.56 

99.6 

06.55 

587 

22.22 

72.7 

1877 

97.7 

51.0 

60.70 

8 

21.5 

08.73 

tZOI.  3 

0671 

60.3 

22.35 

77.5 

1894 

99.3 

/6.52 

6136 

9 

//224 

(08.90 

2202.9 

106.87 

2/6/.S 

423.46 

//74.4 

J19.I2 

23009 

1/669 

2254  / 

46101 

/0 

23.2 

09.06 

04,5 

07.03 

63.4 

Z4.ll 

7f.3 

19.29 

02.6 

16.86 

55.6 

62.67 

H 

24.  / 

09.23 

06.2 

07.19 

64.9 

24.74 

76.1 

19.47 

O4.2. 

17.03 

571 

63.33 

/£ 

25.0 

09.40 

07.8 

07.35 

66.4 

25.37 

77.0 

19.64 

05.8 

I7./9 

587 

63.  98 

13 

25.8 

09.  56 

09.4 

07.51 

68.0 

26.00 

77.9 

07.5 

17.36 

60.2 

64.64 

/4 

26.7 

09.73 

II.  / 

07.67 

69.5 

2643 

1939 

09.1 

/7.S3 

61.7 

65.30 

IS 

276 

09.90 

/2  7 

07.23 

71.1 

27.26 

79.(> 

20.17 

'0.7 

17.70 

63.3 

6594 

/& 

294 

10.06 

14.3 

07.99 

72S, 

27.09 

90S 

124 

17*7 

64.8 

6&62 

17 

29.3 

IO.Z3 

16.0 

08.15 

742 

2*52 

20.52 

140 

12.03 

66.3 

67.27 

3o.i 

/0.4O 

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08.31 

7S.7 

29.  IS 

82.Z 

20.69 

IS.G, 

679 

67  93 

/9 

113  1.0 
3/.9 

110.57 
10.73 

2219.2 
20.9 

03.64 

2,177.2 
79.9 

429.79 
3041 

83.9 

21.04 

23/73 
19.9 

U837 
W.S4 

2269.4 

70.9 

468.59 
6925 

20 
2.1 

32.8 

10.90 

22.5 

08.80 

$0.3 

31.06 

21.22 

20.5 

19.71 

7t.S 

69.9' 

ZZ 

33.6 

II  O7 

24.2 

08.96 

81.9 

3/.69 

95.7 

21.40 

ZZ.Z 

18.88 

74.0 

70.58 

23 

345 

11.24 

25{? 

09.12 

634 

32.32 

86£> 

21.57 

Z3.8 

I9.0S 

755 

24 

35.4 

11.41 

27.4 

09.19 

84.9 

3?  96 

874 

25.4 

19.11 

77.0 

7I9O 

W 

362 

11.58 

29.  / 

09.44 

36.5 

336O 

21.92 

27.  / 

/9.18 

786 

7256 

26 

37.1 

11.74 

J0.7 

09.61 

89.0 

34.23 

99.2 

22.10 

297 

19.  55 

8o.l 

7J.23 

27 

32.0 

11.91 

32.3 

09.77 

896 

34.87 

90,0 

22.28 

303 

19.  72 

81.6 

73.29 

23 

38.8 

'2.08 

».o 

09.9} 

91.1 

35.51 

90.9 

22.45 

32.0 

19.99 

83.Z 

74.55 

£9 

1139.7 

112.25 

2235.6 

110.09 

2192.6 

4-36.14 

1/9  /•? 

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2333.6 

\VDjO6 

2284.7 

473T22- 

30 

40'6 

'2.42 

372 

IO  ?6 

94.  Z 

36.78 

22.81 

35.2. 

20.23 

86.1 

7SB8 

31 

41.4 

12.59 

38.9 

10.41 

95  7 

37.4Z 

93.5 

22.99 

36.9 

2040 

97.7 

76.55 

3Z 

42.3 

12.76 

40.5 

/O.S8 

973 

38.06 

94.4 

23J6 

20.57 

89.3 

77.21 

33 

43.2 

12.93 

42.1 

1074 

98.8 

38.70 

9S.Z 

23.34 

40.1 

20.74 

908 

34 

44o 

n.io 

43.8 

tO  9/ 

2200.3 

39.34 

96.1 

23.52 

4-1J8 

20.9/ 

5123 

~7S  5*5" 

44.9 

13.27 

454 

//.07 

01.9 

39.98 

97.0 

23.70 

43.4 

21.08 

9*9 

79.  11 

36 

45.8 

/3.44 

470 

//  23 

03.4 

4o.62 

979 

23.27 

21.25 

93-4 

7928 

97 

46£ 

13.61 

42.7 

11.40 

O5.0 

4/.26 

24.05 

46k 

21.42 

969 

80.55 

47.5 

13.78 

&3. 

//.56 

06.5 

41.90 

99.6 

24.23 

48.3 

11.59 

98* 

81.22 

39 

114-8.4 

113.95 

2251.9 

///73 

2208.0 

44254 

/200.5 

124.41 

2349.9 

111.77 

23000 

481.88 

40 

49.2 

14.12 

Si  6 

1129 

09.6 

43.19 

01.3 

2459 

SI.  5 

21.94- 

01.5 

92.55 

4-1 

£oj 

14.19 

55.2 

12.05 

//    / 

OZ-.Z 

24.77 

53.2 

22.11 

03.0 

83.22 

4-t 

SI.O 
51.8 

1446 
14.63 

IIJ 

/2tt 
/232 

12.6 
14.2 

4447 
45.12 

03.1 
03.9 

24.94- 
25.12 

S4.S 
56.4 

22.22 
2245 

04.5 
06.\ 

83.89 
84.56 

4-3 

4-4 

52.7 

I4.d0 

601 

/2.S5 

157 

45.76 

048 

25.30 

581 

2XJ6Z 

07.6 

4S 

53.6 

14.97 

6/J 

/2.7I 

17.3 

4641 

05.7 

ZS  48 

597 

22.79 

09.1 

?5.9? 

44, 

54.4 

/5.I4 

634 

47.05 

06.6 

Z5\b6 

61.3 

22.96 

10.6 

86.58 

4-7 

55.3 

15  3/ 

65.0 

/3.04 

20.3 

47.70 

074 

25.84 

63.0 

23.14 

122 

9725 

49 

56.2 

15.43 

66.6 

13.20 

2/.9 

48.34 

08.3 

26.02 

64.6 

23.31 

13.7 

8792 

49 

J/570 

115.66 

2268.3 

1/3.37 

22234 

442.99 

/2.09.2 

12620 

2*662 

123.48 

23/512 

499.60 

So 

57.9 

15.83 

69.9 

13  53 

24.9 

49.64 

lO.o 

26.39 

67.9 

23.65 

'6.7 

89.27 

fl 

58.8 

16.00 

7/5 

/3.70 

2.6.5 

50.28 

10.9 

26.56 

69.5 

9994 

52 

59.6 

16.17 

73.Z 

13.96^ 

Z2.o 

50.93 

IIS 

26.74 

71.1 

24.00 

19.2 

90.6Z- 

53 

6(4 

16.35 
16.52 

74.8 
76.5 

14.20 

31.1 

52.23 

12.6 
13.5 

26.92 
27/0 

72.7 
74.4 

24.17 
2434 

Z<3 
222 

9/.M 
9/97 

54 
SS 

62.? 

16  69 

78.  1 

14.36 

32.6 

52.88 

I4A 

27.2g 

7*0 

24.52 

24.4 

9^.65 

S6 

63.1 

16.86 

79.7 

14.53 

$4.  1 

S3.S3 

27.46 

776 

2469 

159 

9J.3Z 

S7 

64.0 

17.04 

81.4 

14.69 

35.7 

16.1 

27.64 

79.3 

24.26 

274 

94.00 

SV 

64.8 

17.21 

83.0 

J4.8& 

372 

5A**> 

I7A 

Z7.8Z 

809 

289 

9468 

59 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


, 

24° 

25° 

T 

E 

C 

M 

X 

Y 

T 

E 

C 

M 

y 

Y 

0 

IZI7.9 

1*8:00 

•23825 

\25.tl 

2330.S 

49F.3/ 

1  17O  "2. 

f39.H 

E400.Z 

115.82 

2421.5 

53682 

1 

J8.7 

28.19 

84.2. 

25.38 

32.0 

96.03 

71  1 

39.30 

81.9 

36.00 

23.0 

3/53 

z 

19.6 

29.37 

gs.z 

2555 

33.5 

72.0 

39.49 

83.  S 

36.18 

245 

3 

20.5 

28.55 

<&7.4 

25.73 

35  O 

97:39 

39.68 

8  S.I 

36.36 

26.0 

3094 

A 

21.4 

28.73 

89.0 

25.90 

36.  5 

98.  07 

73.7 

39.27 

86.8 

3654 

275 

39.64 

5 

222 

2?.9/ 

90.7 

26.07 

38.1 

98.75 

74.6 

40.06 

88.4 

36.72 

29.0 

4035 

6 

23.  / 

29.09 

92.3 

26.2f 

39.6 

99.43 

75.5 

40.25 

90JO 

36.90 

305 

4/.06 

7 

2.4.0 

29.27 

93.9 

26.42 

fOO.II 

76.4 

9L6 

37.08 

32.0 

4A76 

8 

24  § 

29.45 

956 

26.60 

42.6 

00.79 

77-z- 

40.63 

93.3 

32  26 

33.5 

42,47 

9 

257 

29.64 

972 

26.77 

44.2 

01.47 

40.82 

94.9 

37.44 

35.o 

/o 

'226  fe 

129.82 

2398  S 

JZ6.95 

2345.7 

502.16 

/279.0 

14-101 

24965 

/  37.63 

24366 

543.89 

// 

27.5 

30.00 

240015 

27/2 

472 

02.84 

70.9 

4/.'*0 

98J 

378/ 

3S.I 

44.60 

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28.3 

30.19 

02  ( 

27.39 

48.7 

03.52 

90.7 

4/.39 

99.8 

3799' 

39.6 

4S.3I 

/3 

29.2 

30.37 

03.7 

27.47 

50  Z 

04.20 

6V.6 

41.58 

250/.4- 

3RI7 

41.1 

46.02 

14 

3O.I 

30.55 

05.3 

2764 

51.8 

04.89 

52.5 

41.75 

03.0 

38.35" 

42.6 

46.73 

/5 

309 

30.74 

O7.0 

27.82 

5J!3 

05.57 

83.4 

4/.97 

046 

38.53 

44.1 

47.44 

3/.F 

30.92 

086 

2799 

06.26 

84.2 

42.  16 

06.3 

3872 

456 

48.15 

/7 

32.7 

31.10 

/0.2 

28.  »7 

56.3 

06.94 

42.35 

07.9 

38.90 

47.  / 

48.86 

/£ 

33.6 

3/.Z9 

/A9 

28.34 

578 

07.63 

86.0 

42.54 

09.5 

39.08 

486 

49.57 

(9 

34.4 

31.47 

/J.5 

28.  SZ 

J-9.4 

08.  3/ 

#6.9 

42.73 

11-2 

39.26 

SO.I 

sort 

2o 

J235.3 

/3/  65 

24/5J 

IZ9.70 

2360.9 

509.00 

1287.7 

/42.9Z 

2SI28 

/3945 

245/6 

551.00 

2/ 

36.2 

31.84 

/6.7 

2887 

62.4 

09.69 

43.J2 

14.4 

39.63 

53.; 

51.71 

22 

370 

32.02 

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29.05 

63.9 

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89.'5 

43.31 

16.0 

39.81 

54.6 

52.43 

Z3 

379 

32.20 

2o.o 

29.22 

65.4 

11.06 

43.50 

177 

40.00 

56  / 

53.14 

24 

388 

32.39 

2/.6 

29.4<J 

66.9 

;;.75 

9l'.2 

43.69 

19.3 

40.18 

576 

S3.8S 

25 

39.7 

3257 

23.3 

29.58 

68.5 

A?.44 

92.  ; 

43.89 

?0.9 

40.36 

59.2 

g57 

26 

405 

32.76 

24.9 

29.75 

70.o 

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9*0 

44.0g 

22  5 

AO.SS 

60.7 

29 

27 

4/.4 

32.94- 

26.5 

29.93 

71.5 

^3.82 

93.9 

44.27 

2A2 

40.73 

62.Z 

56.00 

28 

42.3 

33.13 

30.\o 

730 

1451 

54.7 

4447 

25.8 

40.91 

63.7 

56.71 

29 

43.2 

33.31 

29.8 

30.2.8 

74.5 

15.20 

9S.6 

44.66 

274 

4/.IO 

65.2 

57.4$ 

30 

IZ44.0 

133.50 

2431.4 

1  30.46 

23760 

5/5.89 

/296.5 

J44.85 

2529.0 

/4V  28 

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90.30 

Z/.6 

4g.S7 

ft 

62.Z 

83.64 

3i7 

7794 

45.7 

700.71 

MX 

97.07 

30.5 

90.52 

3JP 

4-9.40 

39 

63.1 

83.*6 

35.3 

78.15 

47/ 

01.51 

/65 

97.30 

?2.l 

ft>.73 

34.5 

S0.2Z 

4o 

/464.0 

124.08 

2836.9 

178.  35 

Z7486 

70  2.3  / 

/5/74 

197.53 

2933.7 

/  90.94 

2835.9 

757.05 

4j 

649 

84.30 

38.5 

78.5(, 

50  « 

03JI 

/8.3 

97.75 

35.3 

9/./6 

374 

J-/87 

A2 

65.8 

84.52 

40.1 

78.77 

5-/5 

03.9) 

/9.2 

9Z9? 

36.9 

9/-37 

388 

5170 

43 

66.7 

84.74 

41.7 

78.97 

53.0 

04  7/ 

20.) 

9?.!' 

38.5 

•9/.W 

40.3 

5351 

44 

67-6 

84.96 

434 

79.,  8 

54.4 

05.F/ 

2)0 

98.44 

40.1 

31.90 

41.7 

54.35 

4? 

6»5 

85.18 

45.0 

7939 

559 

06.31 

2)9 

98.67 

417 

92.01 

43.1 

55.17 

46 

69.3 

8540 

46.6 

79.59 

574 

07.11 

22.8 

9g.90 

433 

92.Z? 

44.6" 

5600 

47 

70.2 

8563 

A8.Z 

79.80 

58.8 

07.91 

23.6 

99.13 

4S.o 

9244 

460 

56.83 

48 

7/J 

05.R5 

#)X 

90.01 

60.3 

08.72 

245 

99.36 

46  6 

9265 

47.5 

J7.66 

49 

72p 

86.07 

5J.4 

80.21 

61.7 

09.52 

.    2x4 

99.59 

4F> 

92>7 

4&9 

58.49 

5-0 

(472.9 

186.29 

285*0 

/  80.42 

2765.2 

7/0.33 

/S263 

J99.82 

2549.8 

/9J-08 

28504 

759.32 

5V 

73.8 

86.51 

J4.7 

80.63 

64.7 

//./3 

272 

20oo5 

5/-4 

93.30 

5/.tf 

60./4 

52 

74.7 

86.73 

563 

So.g4 

66  / 

11.9) 

28.1 

00.28 

53.0 

9?.5) 

53.3 

60.97 

53 

7T6 

8695 

579 

8/.05 

67.6 

'2.74 

29.0 

00.51 

546 

95.73 

54.7 

(,1.90 

34 

7£5 

97.17 

^59.5 

gt.25 

69.0 

/3S4- 

29.9 

0074 

562 

93.94 

F6.2 

62.64 

5f 

77.3 

8740 

61.  1 

81.46 

705 

/4.3S 

30.8 

00.97 

578 

94/6 

576 

6j[47 

56 

791. 

8762 

62.7 

8/67 

72.0 

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3/7 

0/.20 

59.4 

94.37 

590 

64.30 

57 

79.1 

87.84 

643 

81.38 

7J.4. 

^5.96 

32.6 

0/.43 

61.  / 

9459 

605 

65J3 

58 

80.0 

88.06 

66.0 

82.09 

74.9 

/677 

33.5 

0/.66 

627 

94.90' 

6J.9 

65.96 

59 

80.9 

88.23 

676 

»2.29 

7«.3 

/7.5» 

3AA 

oi.89 

64.3 

95.02 

614- 

66.79 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


30° 

3\° 

/ 

r 

E 

c 

M 

X 

V 

T 

E 

C 

M 

X 

Y 

1535  3 

202.12 

2965.9 

(9523 

2864.8 

767.63 

1589.0 

Z/625 

30624 

208.38 

295V.  0 

<3/838 

O 

36.  / 

02.  35 

675 

95.45 

66.3 

68.46 

89.9 

16.49 

64.0 

08.6,1 

524 

79.24 

1 

37.0 

02-?? 

69.  / 

9566 

6Z7 

69.30 

908 

/6.73 

65.6 

08.83 

S3.8 

2JD.IO 

2. 

379 

02.8/ 

70.7 

95.88 

69.? 

70.13 

9|.7 

/6.97 

672 

09.05 

55.3' 

20.96 

3 

38.8 

OJ.05 

72.3 

96/0 

70.6 

3296 

92.6 

/7.2I 

68.8 

09.28 

567 

ZI.8Z 

4 

39.7 

03.29 

7J.9 

96.31 

72  .0 

7igo 

935 

/74F 

70.4 

09.50 

58.1 

226? 

S 

406 

0351 

7S-.5 

%5) 

7.3.5 

72.  V 

94> 

17.69 

72.0 

09.72 

59.6 

23.54 

6 

41.5 

0)74 

77.2 

96.75 

74.9 

73.47 

95.3 

(7.93 

736 

09.95 

61.0 

24.40 

7 

41.4 

03.97 

7£8 

96.96 

764- 

74.31 

362 

I9.H 

7S.Z 

10.17 

624 

2?.26 

8 

43.3 

04.21 

80.4 

97)ff 

77.* 

7/./^ 

971 

/8.4I 

763 

10.39 

6A8 

26./2 

9 

1544  Z 

204.44 

2.982P 

19740 

2S75.Z 

775.9? 

15-98.0 

Zt$,66 

30784 

2/0.62 

29653 

926.99 

/O 

45:  / 

<?4.67 

83.6 

97.6  / 

£0.7 

76.8r 

98.8 

IS.90 

80.0 

10.84 

66.7 

27.8J 

II 

A6o 

04.90 

8S.2 

97.93 

*2'./ 

77.66 

99.7 

/9I4 

8/.6 

11.07 

681 

2S.7' 

IZ 

46.9 

05.  /  4- 

86.8 

92.05 

*3.6 

7&50 

1600.6 

/9.«8 

93.2 

It.  29 

69.5 

2.9.58 

13 

47.8 

05.37 

88.4 

99.1$ 

85.o 

7?.  33 

015 

19.61 

843 

/LSI 

71.0 

304.4- 

14 

4g7 

05.60 

900 

98.48 

86.4 

80.  /  7 

02.4 

I9.fr 

96.4 

11.74 

72.4 

31.30 

Af 

496 

Of.  84 

9\.<o 

98.70 

979 

91.01 

03.3 

10.11 

88.1 

11.96 

73$ 

3L.I7 

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50.4 

06.07 

93.2 

<?8.K 

P9.J 

81.85 

04  Z 

20.3S 

99.7 

/t.>9 

75-.Z 

33.03 

17 

5/3 

06.30 

949 

99.)  3 

90.? 

82.70 

05.  / 

20.59 

91.3 

12.41 

76.7 

3*90 

>8 

SZ.z 

06.54 

96.5 

99.35 

92.2 

83^4 

06.0 

20.83 

923 

12.64 

78.1 

54.77 

J9 

tr&.i 

206.77 

299S./ 

199.57 

2893.6 

7g*.3g 

1606.9 

21.\JDZ 

3094.5 

2/2.86 

29725 

£35:63 

ZO 

S~4.0 

07.01 

99.7 

99.79 

95./ 

95.  2  a 

07.? 

2/.31 

96.1 

13.09 

80.9 

36.50 

2/ 

5-4.9 

07.24 

?00'.  3 

zoo  oi 

96.5 

86.06 

087 

•21-56 

97.7 

/3.3I 

814 

37.37 

22 

55.8 

07.4? 

02.9 

00.  22 

9£/> 

86.90 

09.6 

21.80 

99.3 

13.54 

8.3.8 

3^23 

23 

56.7 

07.71 

045 

00.44 

99.4 

07.75 

lO.S 

22.05 

3/009 

13.76 

85.2. 

3910 

24 

57.6 

07.90- 

06.1 

0C.6(> 

Z90S8 

5^.5"9 

11.4 

2229 

025 

1339 

86.6 

3297 

25 

585 

08.18 

077 

OO.S2 

02.3 

^94^ 

12.3 

22.53 

04.1 

14.21 

88.0 

46.&1 

26 

59.4 

08.41 

09.3 

01.  to 

03.7 

90.a8 

132 

2?.7* 

05.7 

W.4A 

89.5 

41.71 

27 

60.3 

08.65 

109 

0/.32 

0y./ 

Jilt 

14.1 

Z\0l 

073 

/4.67 

90.9 

42.58 

28 

61.2 

08.98 

125 

01.54 

06.6 

91.97 

ISO 

2i.27 

08.9 

/4.89 

~9t.3 

43.45- 

29 

IJ62  1 

209/2 

30/4  Z 

10/.76 

2902.0 

792.32 

K>/s:9 

223.5) 

31105 

2/5/2 

2993.7 

844.32 

30 

63.0 

09.36 

15.8 

0/.98 

095 

93.66 

16.8 

23.75 

IZJ 

/5.34 

95.2 

45"  /9 

3/ 

63.9 

09.5"9 

17.4 

OZ.\9 

io!9 

94.5' 

17.7 

24.00 

13.7 

/S57 

96.6 

46.06 

32 

64.8 

09.83 

19.0 

024-1 

/2.3 

95J36 

/8.6 

24.24 

15.3 

15.80 

\8P 

46.93 

33 

65.7 

10  Of, 

206 

02.63 

«.g 

%.2o 

19.5 

24.49 

169 

1602 

%.4 

47$l 

34 

66.6 

10.30 

22.2 

02.85 

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9705" 

20.4 

24.7^ 

13.5 

16.25 

3000.9 

4868 

35 

67.5 

10.53 

23.8 

03.07 

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979o 

2/3 

24.9? 

20.1 

16.42 

02.3 

4-9.5? 

36 

68.4 

10.77 

25.4 

03.29 

/«/ 

98.75 

2Z2 

•  25.22 

21.7 

16.70 

03.7 

S0.43 

37 

69.2 

11.01 

27.0 

03.51 

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9960 

2?.l 

25.47 

23.3 

16.93 

OfJ 

S/.30 

38 

7*.' 

//.Z5 

23.6" 

03.73 

20.9 

800.45 

24.o 

2S.7/ 

25.0 

17.16 

065 

52/7 

39 

>57/.o 

Z//.4S 

3030.2 

203.95 

29224 

8o/.3o 

;6Z4.9 

2Z5.96 

3/2.6.6 

21739 

3007.9 

853.05 

40 

7/9 

II.T2 

31.8 

04.17 

23.8 

02.15 

25.8 

26.21 

282 

'7.6  / 

094 

53.92 

4-1 

72.8 

11-96 

33.4 

04.39 

25.2 

03  oo 

267 

26.45 

29.  8 

17.94 

10.2 

54.8o 

42 

73.7 

IZ.I9 

WJ 

04.62 

26.7 

03.95 

276 

26.70 

31.4 

18.07 

le.z 

55.68 

43 

3*6 

/2.43 

36.7 

<?4.g4 

2ff.( 

0470 

28.5 

26.94 

33.0 

18.30 

13.6 

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44 

2T5 

/Z.67 

38.3 

05.06 

295 

05.55 

29.4 

27.  /  9 

346 

18.52 

ISO 

-5-743 

4f 

76.4 

tZ9l 

#9 

05-28 

3/o 

06.40 

3o.3 

27.44 

36.2 

19.7* 

'64- 

S83I 

46 

773 

/3.I4 

41.5 

05:50 

524 

07.26 

31.2 

2768 

37.8 

18.9? 

/7.9 

59.  )8 

47 

78.  Z 

/3.38 

43.1 

05.  7  Z 

33.9 

08.11 

32.1 

2793 

39.4 

19.  Zl 

/9.3 

60.06 

48 

79.  / 

/3.6Z 

44.7 

0594 

35.3 

08.96 

33.0 

^28.18 

4l.o 

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20.7 

60.94 

49 

;  58».o 

i/3.86 

3046.3 

206  If, 

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9o9.se 

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2Z9.42 

3/4-2.6 

2/9.67 

3022  1 

?6/.£2 

SO 

?0.9 

I4.io 

479 

06.39 

38./ 

/o67 

34.8 

2867 

44.2 

19.89 

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62.70 

51 

8/.8 

1434 

49.5 

06.61 

^9.6 

H.S3 

35.7 

28.92 

45.8 

20.12 

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63.f8 

52 

82.  7 

14.57 

51.1 

06.83 

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36.6 

29./7 

474 

20.35 

26.4 

6446 

5J 

8t.6 

1431 

52.7 

0705 

424- 

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37.5 

29.41 

49.0 

20.  59 

27.? 

65.34 

54 

va.s 

15.05 

543 

0727 

438 

14.09 

38.4 

2966 

50.6 

20.81 

29  Z 

66.22 

55 

85.4 

/5.29 

55.9 

0749 

453 

W.9f 

39.3 

29.91 

52.2 

21.04 

30.6 

67.10 

5^ 

96.3 

/5.53 

575 

07.72 

46.7 

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40  2 

30.16 

53.8 

2/27 

32.0 

67.98 

57 

872 

'5.77 

59.a 

07.94 

4g.  / 

16.67 

41.1 

30.40 

55.4 

21  5o 

33.4 

6g$7 

58 

88.1 

/6.0/ 

(,o.S 

OS.  16 

A9.6 

/7.52 

42.0 

30.65 

57.0 

21.  73 

34.8 

6975 

W 

28 


TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

3£° 

3J° 

T 

E 

c 

M 

X 

y 

T 

E 

C 

M 

X 

Y 

o 

1643.0 

23090 

3158(3 

221.96 

30363 

870.63 

(697.  2 

246.08 

3254.6 

23595 

31206 

924-36 

( 

439 

31.  If 

60.2 

2Z.I9 

377 

71.  S? 

98.7 

4634 

562 

36./9 

220 

25.27 

2 

448 

37.40 

61.$ 

^^.4z 

39.  / 

72.40 

99.0 

46.60 

57? 

36-4? 

23.4 

26.18 

3 

45.7 

37.65 

63.4 

22.65 

405 

73.28 

99.9 

46M 

f9.4 

36.6k 

14.8 

27.09 

4 

466 

37.90 

6X0 

Z2.S5 

4/.9 

74  17 

1700.8 

47  II 

61.0 

3690 

26.2 

28.00 

5 

47.5 

32  J5 

66.6 

23.11 

443 

75.05 

01.7 

47.37 

626 

37'3 

27.6 

28.90 

6 

48.4 

32.40 

68.2 

23.34 

44.7 

7f94 

02.6 

4763 

64  .Z 

3737 

29.0 

29  H/ 

7 

493 

32.65 

69.8 

23.57 

46.1 

76.82 

03.5 

4789 

658 

3767 

304 

30.72 

8 

J-0.2 

32.99 

71.4- 

23.20 

476 

77.  71 

04.5 

49.15 

6J.4 

3785 

3  IS 

31.64 

9 

5V./ 

33.14 

7J.O 

24.03 

49.0 

78.60 

05.4 

48.41 

,69.0 

^8.08 

33.Z 

32.55 

to 

/652o 

23339 

3174.6 

224.26 

3050.4 

879.48 

1706.3 

Z48.U, 

3270.6 

23#.32 

31346 

93^.46 

II 

52/3 

33.64 

76,-i 

24.49 

S/.8 

80.37 

07.2 

489? 

722 

39.56 

36.0 

34.37 

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53.8 

33.90 

77.8 

24.72 

S3.z 

87.26 

08  1 

49.18 

738 

38.80 

37.3 

35.28 

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54.7 

34.15 

79.4 

24.95" 

546 

82J5 

O9.o 

49.44 

754 

39.04 

38.7 

36.ZO 

14 

55:6 

5440 

8i.o 

25.  18 

56.0 

W04 

09.9 

4970 

77<? 

39.27 

44.  / 

37.77 

If 

S€.S 

34.65 

82.6 

25.42 

^74- 

8*93 

lo.8 

4996 

786 

39.51 

41.5 

38.0? 

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57.4- 

34.90 

84.2 

256f 

S8.8 

84  81 

II.  7 

Jo.?2 

8o.t 

39.75 

42.9 

3£94 

17 

5-8.3 

35.  15 

858 

25".  99 

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85.70 

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50.48 

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3999 

44-3 

3?.  85 

/8 

55.2 

35.40 

874 

26  // 

61.7 

86.59 

13.5 

50.74 

834 

40.23 

4-5.7 

40.77 

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6o./ 

55.65 

89.0 

26.34 

63.1 

87.4-9 

t4.4 

Si.  00 

05.0 

4^.47 

47.1 

41.69 

20 

/66/.0 

235.90 

3/90.6. 

226.57 

30645 

888.38 

I7/S.3 

251.26 

32866 

240.7  / 

3/48.5 

94Z.(,0 

21 

6/.9 

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922 

26  .8  f 

659 

89.27 

16.3 

SI.  52 

£70.2. 

4094 

49.9 

43.5  \ 

22 

6E.8 

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93.8 

27.04 

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90.16 

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51.78 

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4/18 

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23 

63.7 

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95:4 

2727 

68.7 

91.05 

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91.4 

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52.7 

45.35 

24 

64.6 

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97.0 

2750 

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91.95 

19.0 

52.30 

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54.  / 

46.26 

25 

65.5 

37/6 

98.6 

27.74 

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91.94 

19.9 

52.57 

945 

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47.  '8 

26 

66.4 

37.4/ 

3100.2 

2797 

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93.73 

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J2.«3 

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42|4 

56g 

48.io 

27 

67.3 

37.67 

01.2 

28.20 

74.3 

94.63 

21.7 

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977 

42.3? 

582 

49.02 

28 

68.2 

37.92 

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28.4-3 

757 

9552 

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993 

42.62 

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49.94 

29 

69.  1 

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28.67 

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50.  £6 

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3078.5 

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951-78 

37 

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29.  /  3 

79.9 

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25.3 

54/3 

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6?.  8 

52,70 

32 

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38.H 

09.8 

29.37 

81.3 

99.10 

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54.40 

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4-3.58 

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53.62 

33 

72.8 

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29.60 

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54.66 

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59.54 

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28.7 

54.92 

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lo.5 

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69.4 

56.38 

36 

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03.59 

30.8 

55.71 

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58.23 

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77.3 

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04.49 

31.7 

55.97 

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7J.5 

59.15 

39 

782 

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05.39 

32.6 

5424 

76.9 

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74.9 

60.07 

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1679.  1 

Z4o96 

32226 

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30926 

906.29 

1733.5 

256.50 

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3176.3 

960.99 

4(- 

80.0 

41.22 

24.2 

31.47 

94-0 

07.19 

344 

56.76 

2o.  / 

45.75 

77.7 

6192 

42 

80.9 

41.47 

25.8 

31.11 

95.4 

08.09 

35.3 

5703 

27.7 

45.99 

79.1 

62.84 

43 

81.2 

4-1.73 

27.4 

3/.94 

96.8 

08.99 

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5729 

23.? 

46.23 

805 

63.77 

44 

St.  7 

41.99 

29.0 

3Z./8 

98.2 

0989 

372 

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249 

46.4? 

87.8 

64.69 

45 

83.6 

42.24 

30.6 

32.47 

996 

/o.79 

38.  / 

5782 

265 

46.72 

83.2 

65.  « 

46 

84.5 

4Z.49 

32.2 

32.65 

3101.0 

11.63 

39.0 

58.08 

28  / 

46.96 

84.6 

6655 

47 

85.4 

4Z.7$- 

33.8 

32.88 

02.4 

/Z.S9 

39.9 

58.35 

29.6 

47.20 

86.0 

67.47 

4? 

8*.3 

43.00 

35.4 

33.  IZ 

03.8 

ll.So 

40% 

58.67 

31.2 

47.44 

874 

68.40 

49 

87.2 

43.26 

37:0 

33.35 

05.Z 

74.40 

A\.l 

5&88 

323 

47.6"9 

88.8 

69.33 

J-o 

/  688.1 

243.S2 

3238.6 

23}.S9 

3/06.6 

9/5.30 

1742  £ 

S59./4 

3334.4 

24793 

3190.1 

97026 

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89.1 

43.7/ 

40.  Z 

33-92 

og.o 

/6.Z' 

435 

594-/ 

36.0 

A8/7 

91.5 

7/.I8 

52 

9oo 

44.03 

4/.8 

34.0G 

09.4 

/7/7 

44.4 

59.(,7 

376 

A?.*-; 

92.9 

72.11 

53 

90.9 

44.28 

43.4 

34.Z9 

/o.8 

J8.02 

454 

59.94 

39.2 

4g.66 

943 

73.01- 

54 

91.8 

44.54 

45.0 

34.53 

12.2 

/8.9Z 

46.3 

60.20 

4o8 

4^3o 

957 

73.97 

55 

92.7 

44fc> 

466 

3477 

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H.?3 

A7.2 

6o47 

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49.  (4 

97.  / 

7490 

5£ 

93.6 

45.05 

4S.I 

35.00 

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20.73 

48.  1 

60.71 

440 

49.3g 

984 

7/83 

57 

945 

453/ 

49.3 

35.24 

16  4 

Z/.6? 

49.0 

6-t.Oo 

45.6 

4V  6  J 

99.8 

76.76 

59 

95:4 

45.57 

51.4 

&.48 

17.8 

2?.5f 

49.9 

61.27 

47.Z 

49.S7 

3101.? 

77.69 

f9 

%.3 

45.8? 

530 

35.71 

'9.2 

2J.45T 

508 

a.si 

488 

50/7 

02.6 

78.62 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


34° 

'    J5° 

f 

T 

E 

C 

M 

X 

Y 

T 

E 

C 

M 

y 

Y 

/  75"'  .7 

26/  SO 

33S0.4 

^5O.36 

3204.0 

979.56 

1806.6 

2  7$O  5 

34459 

26519 

32864 

/036.2 

0 

52.6 

62.06 

520 

SO  60 

05.4 

80.49 

075 

78.33 

47-5 

6544 

37.2 

1 

53.G 

62.33 

fS.6 

50.85 

06.7 

81.42 

08  4 

7g.6l 

49.  / 

65.69 

89.  / 

38.1 

Z 

54.5 

62.60 

55.2 

57.09 

og./ 

82.35 

09^3 

78.9% 

50.6 

65.94 

90.5 

554 

62.86 

56.8 

5/.33 

09.5 

loZ 

79.16 

66./9 

9/.9 

40.0 

4 

56.3 

63.13 

58.? 

5/58 

/O.9 

84.22 

ll.l 

79.43 

5J8 

66.44 

?J.2 

41.0 

S 

57.2 

5?.  9 

Sl.Qt 

'2.3 

95.15 

IZ.I 

7971 

S5.4 

66.69 

96.6 

4/  9 

6 

£8.1 

63.67 

6/.5 

S207 

/3.6 

86.09 

I3.o 

79.99 

57.0 

66.94 

959 

42.9 

7 

590 

63.93 

63.; 

52.3) 

If.O 

8702. 

/3  9 

90.26 

59.6 

67J9 

97.3 

43.9 

8 

59.9 

64.20 

64.7 

52.56 

/6.4 

8796 

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80.54 

60.2 

6745 

98.7 

44.8 

9 

1760.8 

2-64.47 

33663 

25280 

3217.8 

988.89 

»lf.7 

280.82 

346/.S 

267.70 

33000 

(045.8 

10 

64.74- 

67.9 

5/05 

19.7. 

89.83 

;6.& 

Si.  to 

63.4 

67.95 

46.7 

II 

62.7 

65.0  / 

6A5 

53.29 

20.5 

90.77 

'7.6 

81.37 

64.9 

68.20 

02.8 

47.7 

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636 

65.27 

71.1 

53.54 

21.9 

71.70 

/8.5 

&.6S 

665 

6845 

041 

48.7 

13 

64.5 

65.54- 

72.7 

23.3 

9264 

8/93 

68.1 

68.  71 

05.5 

496 

14 

65.4 

65.81 

74.3 

54.03 

24.7 

9J.58 

20.3 

82*0 

69.7 

68.96 

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50.6 

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66.3 

75.9 

54.27 

26.1 

94.52 

2/.2 

#2.48 

71.3 

6921 

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5A5 

16 

67.2 

66.35 

77.  S 

54.52 

Z74- 

82.76 

72.9 

69.46 

096 

SZ.S 

17 

66.62 

791 

54.76 

28.8 

96.40 

23!' 

83.04 

745 

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10.9 

53.5- 

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69.1 

66.89 

80.6 

ff.OI 

30.2 

37.34 

24.0 

8i.3Z 

76.' 

69.97 

12.3 

J4.4 

19 

1770.0 

267/6 

3382Z 

ZSS.Z5 

323J.6 

998.28 

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£83.60 

3477.7 

27022 

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tOSS.  4 

20 

70.9 

67.43 

83.8 

55.50 

329 

99.2Z 

25.'« 

83.87 

79.2 

7o.47 

ISO 

S64 

zl 

71*. 

67.70 

?574 

55.75 

343 

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26.7 

84  15 

80.8 

70.  7  i 

16.4 

57.3 

22 

727 

67.97 

87.0 

5599 

35.7 

01.' 

27.6 

84.43 

824 

70.98 

17.7 

£8  3 

23 

736 

68.24 

88.6 

5624 

37.1 

02.0 

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84.0 

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19.1 

f9  } 

24 

745 

68.57 

902 

56.49 

38.4 

03  O 

29.5 

8499 

85.6 

7/49 

204 

60.Z 

25 

7SA 

6876 

91.  S 

5673 

39.8 

03.9 

30.4 

85.27 

87Z 

7/.74 

2/.g 

61.2 

26 

764 

69.05 

93.4 

56.98 

4V.Z 

04.9 

31.3 

85.55 

888 

7A99 

23.2 

62.2 

27 

77.3 

69.32 

95.0 

5723 

426 

05.8 

32.2 

8583 

72.25 

245 

63.  1 

28 

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69.59 

96.6 

57.47 

43.9 

06.8 

33.2 

91.9 

72.50 

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64.1 

29 

1779.1 

269.86 

339S>Z 

257.72 

32453 

}007.7 

J834.I 

286.39 

3493.5 

272.76 

3327.2 

106$  1 

30 

80.0 

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99.8 

3~7  97 

46.7 

09.6 

35.0 

86.67 

95.  / 

73.01 

28.6 

66.0 

31 

80.9 

7<7.40 

340/.3 

58ZI 

48' 

09.6 

359 

86.95 

967 

73.26 

299 

67.0 

32 

BIJ 

70.67 

02.9 

584.6 

49.4 

10.  S 

36.8 

983 

73.51 

31.3 

68.0 

3? 

82.8 

70.94 

04.5 

58.71 

508 

11.5 

378 

97.SI 

99.9 

73.77 

32.7 

699 

34 

83.7 

7/.2I 

06.1 

58.96 

52  t 

12.4 

97.79 

350  1.5 

74.03 

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^5* 

84.6 

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07.7 

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53.5 

396 

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354 

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36 

85.5 

71.76 

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59.45 

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14.3 

40.5 

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74.54 

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86.4 

72.03 

109 

59.70 

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15.3 

4/.4 

89.63 

06.2 

74.79 

38.  / 

38 

873 

72.30 

IZ.S 

J995 

577 

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42.3 

88.92 

07.8 

7S.OS 

39.4 

7/8 

39 

'7F8  2 

272.58 

34/41 

260.20 

3259.0 

\o\7.l 

/84J.3 

289.20 

3509.4 

27530 

3340.8 

1074% 

4o 

89.7. 

72.85 

J5.7 

60.44 

604 

18.1 

44.2 

//.o 

7f.S6 

42.1 

7f.7 

A! 

9o.l 

73.  JS 

173 

60.69 

61.8 

45.  1 

89.76 

7f.Vl 

4.3.5 

76.7 

42 

9l  o 

73.39 

tg.8 

66.94 

63.1 

20.0 

46.0 

90.04 

I4.Z, 

76.07 

44.8 

77.7 

4? 

919 

73.67 

20.4 

6/.I9 

645 

2/.0 

46.9 

90.  H 

IS.7 

76.32 

46.2 

78.  6 

44 

92.8 

73.94 

220 

61.44 

«>5.9 

2/9 

47.3 

9061 

17.3 

76.52 

475 

79.6 

45 

93.7 

74.21 

23.6 

61.69 

673 

229 

488 

90.99 

>8  9 

48.9 

So.6 

46 

946 

74.49 

25.2 

61.94 

68.6 

23.8 

497 

91.17 

205 

77.09 

50.3 

8/6 

47 

9516 

74.76 

26.8 

62.19 

7oo 

24.8 

50.6 

91.46 

221 

77.35 

82.5 

48 

96.5 

7S.03 

28.4 

62.44 

714 

2S.7 

5/.5 

91.74 

23.7 

77.60 

53.0 

49 

17974 

275.  3  / 

3430.0 

262.69 

3272.7 

/026.7 

/852.S 

29202 

3525.3 

27796 

3354.3 

/084.5 

So 

98.3 

7f.58 

31.6 

62.93 

74.1 

276 

534 

92>0 

268 

78.  It 

55.7 

5V 

99.  e 

7586 

33  Z 

63.l# 

75  S 

28^ 

54.3 

92.59 

28.4 

78.37 

570 

86  '.4 

5"2 

tSoo.i 

76.  13 

34.7 

63.43 

768 

29.  f 

55.2 

92.87 

30.0 

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58.4 

87.4 

5? 

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76.40 

363 

63.68 

30.5 

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93.  16 

316 

7S99 

59.7 

98.4 

54 

02.0 

76  .68 

379 

63.93 

796 

57' 

93.44 

33.2 

79.14 

61.1 

89.4- 

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02.9 

76.  9J 

J9.5 

64.  IB 

809 

32.4 

58.0 

93.72 

34.8 

7940 

62.4  j    90.4 

56 

7^3 

41.1 

64.43 

92.3 

ji  3 

58.9 

9401 

364 

79.66 

63.8  I    9Y3 

57 

04.7 

7*50 

A27 

64  6# 

34.3 

59.8 

9429 

379 

79.91 

65.  / 

92  3 

5? 

056 

77.78 

443 

6490 

#5.O 

352 

60.8 

94.5? 

39.5 

9o.i7 

66.5 

93.3 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

36" 

37° 

T 

E 

C 

M 

X 

Y 

T 

E 

C 

M 

Y 

Y 

o 

!&(>!  7 

294.86 

55"4/  / 

280.43 

3367.8 

J094.3 

1917.' 

3/2.2Z 

3636  1 

29609 

34481 

1(537 

1 

62.6 

9514 

42.7 

80.69 

69.2. 

95.2 

I8.o 

X2.52 

377 

495 

54  8 

z 

63.5 

95.43 

44.3 

80.94 

70.5 

96.1 

I9.o 

12.91 

39.3 

9662 

509 

558 

3 

64.4 

95.72 

45.9 

81.20 

71.8 

97.2 

19.9 

13.  10 

40.8 

9688 

56.8 

4 

65.4- 

96  oo 

47.5 

81.46 

73.1 

991 

zog 

13.40 

424 

97.15 

53.5 

578 

5 

66  3 

96*9 

49.0 

8  1.7  -a 

74.  S 

99.2 

21.  7 

13.69 

440 

97.41 

54.8 

58.8 

6 

67> 

96.57 

S0.6 

81.98 

75.9 

lloo.z 

22.7 

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45.6 

97.68 

56.2 

59.8 

7 

68.  / 

96.86 

SZZ 

82.23 

77.2 

01  1 

23.6 

14.18 

47.2 

9794 

57.5 

608 

8 

69.0 

97.14 

S3  % 

Sz.49 

786 

Oi.l 

14.58 

487 

98.Z\ 

58S 

61.8 

9 

7O.O 

97.43 

SS.4 

9175 

79.9 

03.1 

2*5 

14.97 

503 

98.47 

60.2 

6Z.8 

/O 

19709 

297.72 

35-57.* 

Z83.0I 

33g,3 

1104  1 

'9264 

3\5.\7 

36J~/9 

298.74 

346/5 

1163.8 

// 

7/.g 

98.oo 

5"86 

8327 

826 

05.  \ 

27.3 

15.47 

53.  5 

99.  00 

62.8 

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7i  7 

98*9 

60.1 

83.53 

84.0 

06.1 

28.2 

1576 

SS.I 

99.27 

641 

65  8 

/3 

73.7 

9857 

61.7 

83.79 

853 

07.0 

29.2 

566 

99.53 

655 

66.8 

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746 

98.86 

633 

84.05 

8G.7 

08.0 

30.1 

/63S 

S8.2 

99.80 

66.8 

67.8 

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7,5""  5" 

99.15 

64.9 

8431 

880 

090 

31.0 

/6.65 

300.07 

68.1 

688 

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76.4 

99.44 

665 

84.57 

89.3 

10,0 

320 

/6.95 

61.4 

694 

69.8 

17 

77.4 

99.  7j? 

68.1 

84.83 

90.7 

II.O 

32.9 

17.  24 

629 

00.60 

70.8 

70.9 

18 

783 

300.OI 

69.6 

85.08 

92.0 

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33.8 

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645 

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79.  ^ 

00.30 

71.2. 

85.34 

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13.0 

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17.84 

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73.4- 

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1880.1 

300.S9 

3572? 

295.60 

1594-7 

11133 

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3l8.\3 

3667.7 

301.40 

3474.7 

1173.9 

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Bio 

00.87 

74.4 

85.86 

96.1 

J4.9 

36.6 

1843 

69.? 

OI.6J 

76.1 

74.9 

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820 

01.16 

76.0 

96.12 

974 

15.9 

37.5 

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70.8 

01.93 

774 

23 

92.9 

01.45 

77.6 

86.3g 

98.7 

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3g.S 

f9.o3 

724 

02.20 

79.7 

76.3 

14 

839 

01.74 

79.1 

86.64 

34001 

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39.4 

740 

0247 

80.1 

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25 

847 

0203 

80.7 

86.90 

01.4 

18.9 

40.3 

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75.6 

02.73 

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78.9 

26 

25.7 

02.32 

923 

87.16 

19.9 

41.2 

19% 

772 

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80.0 

27 

86.6 

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83.9 

07.42 

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42.2 

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91.0 

28 

875 

02.89 

85.5 

87.69 

05.4 

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43.1 

20.52 

03.54 

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92.0 

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88.4 

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87.9? 

06.9 

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44.0 

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81.9 

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867 

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30 

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303.47 

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91.2 

04.05 

98.73 

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86.6 

04.61 

90.6 

86.0 

33 

92.1 

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93.4 

88.99 

12.1 

47.7 

22.01 

es.t 

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34 

93.1 

04.63 

89.15 

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27.g 

48.7 

22.31 

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933 

88.1 

35 

94.0 

04.92 

96.6 

89.51 

14.8 

28^ 

4-9.6 

22.61 

91-4 

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89.1 

94.9 

05.21 

98.1 

89.77 

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29.8 

50.5 

22.91 

92.9 

05.68 

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37 

OS.So 

99.7 

90.04 

17.5 

Si.  5 

23.21 

94.5 

05.95 

97? 

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3# 

9(..7 

05.79 

3601.3 

90.30 

18.8 

3/'.8 

524 

23.  Si 

96./ 

06.11 

98.6 

92.1 

29 

97.7 

06.08 

02.9 

90.56 

20.2 

32.9 

J3.3 

23.8; 

97.7 

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99.9 

93.2 

40 

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306.37 

3604.5 

290  .9Z 

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)  133.9 

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324.  )/ 

3699.3 

306.76 

350/.Z 

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41 

99.5 

06.66 

06.0 

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228 

348 

55.2 

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37^.8 

07.03 

025 

952 

42 

W00.4 

06.95 

07.6 

91.35 

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35.8 

56.1 

24.71 

02.4 

07.23 

03.8 

96.2 

43 

01.4 

07.25 

09.2 

15.5 

36.8 

570 

2501 

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07.56 

05.2 

97.2 

44 

023 

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10.8 

91.97 

37.7 

58.0 

2531 

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07.83 

06.5 

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45 

03.2 

07.83 

12.4 

91.13 

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38.7 

58.9 

25.61 

07.1 

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078 

99.3 

46 

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09.12 

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29.5 

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08.64 

104 

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17.1 

92.92 

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41.7 

61.7 

26.52 

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49 

06.9 

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187 

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42.7 

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26.82 

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309.29 

3620.3 

293.45 

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1143.7 

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327.  IZ 

37/5.0 

309.45 

3514.4 

120  A.  4 

ft 

09.8 

09  5g 

21.9 

93.71 

36.T. 

44.7 

64.5 

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09.72 

15.7 

05.4 

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93.98 

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457 

6£4 

Z7.7Z 

ft.Z 

09.99 

I7O 

06.4 

53 

/o.6 

250 

94.24 

38.9 

46.7 

66.4 

29.03 

'9.7 

10.  Ik 

'8.3 

07.4 

54 

11.6 

10.46 

266 

94.50 

AO  2. 

47.7 

67.3 

2933 

21.3 

10  5~3 

19.6 

08.5 

IZ  5" 

291 

94.77 

41.'$ 

487 

68.2 

28.63 

22.9 

fo  80 

2/0 

09.5 

5C 

/J.4 

11.05 

29.8 

95.03 

42  9  * 

49.7 

245 

//.  07 

223 

10.5 

57 

14.3 

11.34 

313 

95.29 

44Z 

S0.7 

70  1 

29.24 

11.35 

23.6 

11.5 

S8 

ff.3 

11.63 

32.9 

95.56 

45.5 

51.7 

7/.0 

2954 

276 

II.  & 

249 

/£.(> 

/6.Z 

11.93 

34.5 

95.82 

46.9 

52.7 

7/.9 

29.S4 

29.2 

n.  89 

26.2 

//,6 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


29 


38* 

59° 

/ 

T 

F 

c 

M 

X 

Y 

T 

E 

C 

M 

X 

Y 

19729 

530/5 

J730S 

312.16 

35Z7.S 

IZ/4.6 

2029  O 

348.64 

30252 

3286"4 

3605.8 

\Z76.9 

0 

73.9 

30.45" 

31.4 

/2.43 

^9S 

/57 

29.9 

48.95 

26.8 

28.92 

07.1 

77.9 

1 

74.7 

30.75 

33.9 

IZ.70 

30.2 

/6.7 

30.9 

49.27 

2?.3 

29.20 

09.4 

790 

2 

75.7 

31.  of, 

35.5 

11.97 

3  IS 

^7.7 

31.8 

49.5? 

29.9 

29.4g 

09.7 

80.0 

3 

76.6 

31.36, 

37.1 

13.25 

32.8 

>8.7 

327 

49.89 

31.5 

2976 

H.O 

§1 

4 

77.5 

31.67 

39.7 

/3.S2 

34.  1 

/9.g 

33.7 

fazi 

33.0 

3oM 

/*.? 

1 

5 

78.5 

31.97 

402 

X3.79 

35A 

20.8 

346 

SO.SZ 

34.6 

30.32 

13.6 

2 

6 

79A 

32.27 

41.8 

/4.06 

3B.7 

2/.8 

35.5 

&.84 

36.Z 

30.59 

14.9 

84* 

7 

903 

32.58 

43.4 

14.33 

38.0 

22.8 

36.S 

S/.tS 

37.8 

30.87 

16.1 

85.3 

8 

913 

J2.88 

45.o 

I4.<ol 

39.3 

23.9 

374 

51.47 

39.3 

31.15 

17.4 

963 

9. 

1982.2 

333.19 

374t5 

314.88 

3S40.(> 

/>?24.9 

2039.4 

3f/.7g 

3840.9 

331.43 

36/8.7 

1297.4 

10 

93.1 

33.49 

48.  / 

15.15 

4to 

259 

39.? 

52.10 

42.5 

31.71 

zo  o 

884 

II 

84  / 

33  go 

49.7 

15.41 

43.3 

27.0 

40.2 

52.4  1 

44.0 

31.99 

il.3 

89  f 

ft 

95.o 

34.  M 

5J.3 

IS.  70 

446. 

280 

4f.z 

5Z.K 

45.6 

32.27 

226 

90.5 

/) 

85.9 

34.41 

528 

15.97 

4-59 

29.0 

42.1 

53.04 

472 

#55 

23.9 

9/.6 

14 

86.9 

34-72 

544 

I6.Z4 

472 

3o.  1 

43.1 

5-3.36 

48.7 

3283 

25.2 

92.7 

15 

878 

3S.OZ. 

56.0 

16.  57 

485 

31.1 

44o 

53.67 

50.3 

33.'// 

26.5 

937 

16 

88.7 

3533 

576 

'6.79 

49.S 

32.' 

44'9 

53.99 

5A9 

33.39 

27.8 

949 

n 

897 

J563 

5?/ 

/7.06 

51.1 

J3.2 

459 

S4.30 

53.5 

33.67 

29.1 

9f.8 

/8 

9o.6 

35.94 

60.7 

X7.34 

52.4 

34.Z 

4t» 

S4.6Z 

55.0 

33.95 

3o.3 

969 

19 

19915 

356.25 

37623 

3/76/ 

35  S3  7 

23S.2 

2047.8 

354M 

3856.6 

334.23 

3631.6 

Z97.9 

"20 

9*5 

36.55 

63.9 

/7.W 

550 

363 

55.25 

S8.Z 

34.51 

32.9 

99.0 

21 

93.4 

36.86 

65.4 

/8./6 

S6.3 

373 

f6 

5557 

59.7 

34.79 

341 

I3oo.  a 

22 

94.3 

37.  /7 

670 

/8.43 

57.7 

383 

^ 

5T09 

61.3 

35.07 

35.  5 

01.  1 

23 

95.3 

37  4? 

68.6 

19.70 

59.0 

39.4 

57.5 

56.20 

62.9 

35.35 

36.8 

02  2. 

24 

96.2 

37.7* 

70.  Z 

/8.9B 

60.3 

40.4 

szs 

5652 

64.4 

35.63 

39.1 

03.2 

25 

97.  / 

38.W 

7/7 

/9.25 

6/6 

41.4 

53.4 

56.94 

66.0 

3S.9Z 

39.4 

043 

26 

981 

38.40 

7?.  3 

19  S3 

629 

4Z.5 

543 

57/5 

676 

36.20 

40.6 

05.3 

27 

99.0 

^9.71 

74.9 

I9$0 

64> 

43.  S 

55.3 

5747 

69/2 

36.48 

41.9 

06.4 

28 

99.9 

39.01 

76$ 

20.08 

65:5 

44.5 

5*.  2 

5779 

70.7 

36.76 

43.2 

07.4 

29 

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339.32 

37780 

320.35 

3566.8 

l&f.f. 

20572 

358.11 

3872.3, 

33704 

3644.5 

1308.5 

30 

0/.8 

39.63 

79.6 

20.63 

69.  1 

466 

S8.I 

S8AZ 

73.9 

37.32 

4f.8 

09.6 

31 

ozs 

39.94 

m 

20.90 

69.4- 

47.7 

59.0 

58.74 

7S.4 

37.60 

47.1 

/o.6 

32 

037 

40.25 

82.7 

2/./9 

70.7 

4^.7 

60.0 

59jCX> 

77.0 

37.89 

48.4 

11.7 

33 

04.6 

40.56 

843 

Z/.45 

72P 

49.7 

60.9 

59.38 

78.6 

38.17 

49.6 

12.9 

34 

05-.6 

4087 

85.9 

2A73 

7J.3 

50.9 

6/.9 

59.70 

80.  / 

38.45 

50.9 

13.3 

35~ 

06? 

41.17 

875 

22.«> 

746 

S/.2 

62.? 

6002. 

91.7 

38.73 

52  $ 

14.9 

36 

07.4 

4-1.48 

89.0 

22.tg 

759 

52.9 

63.7 

60.34 

83.3 

39.01 

53.5 

IS.  9 

37 

084 

4/.79 

90.6 

Z2.55 

77? 

53.9 

64.7 

60.65 

84.8 

39.30 

548 

)7-0 

38 

09.1 

42./0 

92.2 

22.93 

78.5 

54.9 

65.6 

60.97 

«.* 

39.  SB 

56.1 

/d.t 

39 

2010.2 

J42.4I 

3793? 

323./0 

3S79.8 

IZS6.0 

2066.6 

361.29 

3898.0 

339.86 

3657.4 

1319  1 

4-0 

\IZ 

42.72 

95.3 

23.38 

31.1 

510 

675 

fel.6/ 

89.5 

4o.  is 

58f> 

20  Z 

41 

12.  1 

4303 

96.9 

23.66 

K4. 

58.1 

68.5 

6J.93 

91.1 

A043 

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21.3 

42 

/30 

43.34 

98.5 

23.93 

83.7 

59.  / 

£9.4 

6Z.Z5 

92.7 

40.71 

61.2 

22.3 

43 

M.O 

43.6? 

3800.0 

24  21 

950 

60.1 

70.3 

62.57 

94.2 

46.99 

62.5 

29.4 

44 

'49 

43.96 

01.6 

24.4? 

863 

6  (.2 

7/.3 

62.89 

95-8 

41.19 

63.9 

24.5 

45 

/*9 

4427 

03.2 

2476 

926 

622 

7£.2 

63.21 

97.4 

4V.56 

65.0 

25.5 

46 

16.8 

44.59 

048 

2504 

88.3 

63.3 

73.2 

63.53 

98.9 

4/.*4 

663 

26.6 

47 

17.7 

449o 

063 

2S.3I 

9°.  Z 

fe43 

74.  1 

63.85 

3900.5 

42.13 

676 

277 

4S 

/ft  7 

45\2I 

07.9 

25.59 

9/.5 

65.4 

75.0 

64./8 

02.1 

42.41 

689 

28.7 

49 

zo/9.6 

345.52 

3*09.5 

325.87 

3592.9 

\2A64 

2.076.O 

364.50 

3903.6 

34Z.70 

3670.2 

13298 

50 

zo.s 

4fg3 

1  l.o 

26.  >5 

94.  / 

675 

76.9 

64  8Z 

052 

42.9* 

7/4 

30.9 

SI 

2f.5 

46.14 

I2f, 

26.4? 

95.4 

685 

77.9 

6514 

06.8 

4326 

727 

31.9 

Si 

2Z.4 

46.45 

/4.2 

26.70 

96.7 

69.5 

7*.  8 

65.46 

08.3 

43.55 

74.0 

33.0 

53 

234 

46.77 

158 

26.9ff 

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70.6 

79.8 

65.78 

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43.83 

753 

34  / 

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24.3 

47  08 

17.3 

2725 

993 

7/6 

80.7 

66.  10 

II.S 

44.1Z 

76.6 

35.  / 

55 

25.  1 

47.39 

189 

27.53 

36006 

72.7 

S/.6 

66.43 

13.0 

44.4o 

778 

36.2 

56 

26.  2 

47.70 

eo.s 

27.91 

01.9 

73.7 

9Z.6 

66.75 

146 

44.69 

79.) 

37.3 

57 

27/ 

48.02 

2Z.I 

2£09 

OJ.t 

74.  f 

8S.S 

67.07 

16.7. 

44.97 

804 

38.3 

58 

28.0 

48.33 

23,6 

2«.37 

045 

758 

84.5 

67.3? 

17.7 

45-26 

8i.7 

39.4- 

59 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

40° 

41° 

T 

E 

c 

M 

X 

V 

T 

E 

C 

M 

X 

Y 

0 

208S-.4- 

367.72 

3919.3 

345.54 

3692.9 

1340.5 

EI42.-Z. 

39738 

40/3.1 

362.85 

3759.0 

1405.4 

1 

864 

68.04 

20.9 

45.83 

#4.2 

4>.6 

43.  Z 

87.7  / 

'4.7 

63.  14 

60.2 

Ob.  5 

1 

873 

6836 

22.4 

46.li 

855 

426 

44.1 

88.04 

/6.2 

63.43 

6/.5 

07.6 

3 

883 

68.69 

24'.0 

46.40 

86Z 

437 

45.1 

88.38 

17.8 

63.72 

62.8 

08.7 

4 

892 

69.o| 

Z5.(, 

46.68 

88.1 

.44.8 

46.0 

88.71 

19.4 

64.01 

64.0 

09.8 

5 

90.1 

69.33 

27.  / 

4697 

893 

45.8 

47.0 

89.04 

209 

64.31 

65.3 

10.9 

6 

91.1 

69.66 

28.7 

4725 

90.6 

46.9 

479 

89.38 

ZZ.5 

64.60 

66.5 

lip 

7 

92.0 

69.98 

30.3 

47.54 

91.9 

48o 

48.9 

89.71 

24.  f 

64.89 

678 

13.1 

8 

3io 

70.30 

31.8 

47.  8Z 

932. 

49.1 

49.9 

90.04 

256 

65.18 

69.0 

14.1 

9 

93.9 

70.  6  3 

33.4 

48.11 

94.4 

fo.l 

So.8 

90.38 

27.2 

65.48 

70.3 

'5.3 

10 

£0949 

370.95 

393f.o 

349.40 

36*5\7 

/3S-/.2 

2IS-I.7 

390.71 

40287 

365.77 

3771.5 

I4l(,4 

II 

9f.8 

7/.Z8 

36.5 

49.68 

97.0 

52.3 

52.7 

91.05 

3o.3 

66.06 

72.8 

'7.5 

11 

96.9 

7/.60 

38.1 

4V.97 

98  Z 

53.4 

S3.  6 

91.38 

31.9 

66.36 

74./ 

/8.6 

1) 

97.7 

7/93 

39.7 

49.26 

99.5 

54.4 

546 

97.72 

33.4 

66.65 

7^.3 

19.7 

14 

98.6 

72.2? 

4/.Z 

49.54 

3700.8 

55.5 

Sf.5 

9205 

35.0 

66.94 

76.6 

248 

IS 

99.6 

72.58 

42  S 

49.83 

C2J 

56.6 

WS 

92.39 

36.5 

67.24 

77.8 

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16 

Z  100.5 

72.90 

44.4 

50.11 

033 

57.7 

57.4 

92.71 

38.1 

67.53 

79.1 

230 

17 

OI.S 

73Z3 

453 

SO*0 

04  (, 

5-0.7 

584 

93.06 

39.7 

67.82 

80.3 

24.1 

18 

02.4 

73.55 

47.5 

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Os.9 

59.8 

59.3 

93.39 

41.2. 

68.  IZ 

81.6 

25.  a 

11 

03.4 

73.98 

49.1 

S0.9* 

07.2 

60.9 

60.3 

93.73 

42.8 

68.41 

82.8 

26.3 

20 

2/043 

374.20 

33*0.6 

357.26 

3708.4 

I36Z.O 

2I61.Z 

394.06 

4044.3 

368.71 

3704.  f 

1427.4 

2/ 

0513 

74.  S3 

52.Z 

SI.S5 

09.1 

63.1 

62* 

94.40 

459 

69.00 

85.3 

285 

2Z 

06.2 

#.86 

53.7 

51.84 

11.0 

64.1 

63.1 

94.74 

475 

69.29 

86.6 

29.6 

23 

072 

7S./8 

SS.3 

5-2.13 

tzz 

65.Z 

641 

95.07 

49.0 

6959 

87.g 

30.7 

24 

08.1 

75.51 

56.9 

S2.4t 

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66.3 

65.1 

95.41 

SO.b 

69.88 

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31.8 

25 

09.0 

7S.84 

584 

5170 

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70.18 

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32.9 

26 

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76.16 

60.0 

52.99 

16.0 

68.5 

670 

96.08 

53.7 

27.47 

9  1.6 

34.0 

27 

/o.l 

76.49 

61-6 

53.19 

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69.5 

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96.42 

55.3 

70.77 

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35.  » 

2* 

11.9 

76.82 

63.1 

53.57 

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70.6 

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96.7* 

56.8 

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94./ 

36.2 

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12.9 

77.  If 

647 

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357.43 

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3/ 

14.7 

77.80 

67.8 

54.43 

224 

73.9 

7/7 

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61.5 

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97> 

39.5 

3Z 

IS  7 

78.13 

69.4 

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23.6 

75.0 

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98.11 

63.0 

72.24 

99.1 

40.6 

33 

lit 

78.46 

71.0 

55.OI 

24.9 

760 

7*6 

98.45 

64.6 

72.54 

38003 

4-1.7 

74- 

176 

78.79 

72.5 

55.30 

262 

77.1 

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66.2 

72.83 

01.  (, 

42.8 

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79.11 

74./ 

55.5$ 

27.4 

78.Z 

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677 

73.13 

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19.  S 

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28.7 

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99.46 

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73.43 

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4-5.0 

37 

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79.77 

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56.16 

30.0 

80.4- 

774 

99.90 

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053 

46.1 

38 

2/.4 

80.10 

TBS 

56.4J 

3/Z 

81  S 

78.4 

4oo.(4 

724 

74  .OZ 

06fr 

47.2 

39 

22.3 

80.43 

80.3 

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32.5 

82.5 

79.4 

00.48 

74.0 

74,3' 

07.8 

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40 

2/23.3 

380.76 

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357.03 

3733.8 

1383.6 

zieo.3 

400.82 

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374.61 

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81.09 

93.5 

57.32 

35.0 

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81.44. 

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57.61 

36.3 

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11.5 

57.7 

43 

261 

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866 

57.90 

37.6 

86.9 

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7S.SO 

12.8 

52.8 

44 

27.0 

82.08 

88.1 

58.19 

38.8 

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04.1 

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7S.SO 

lH-.o 

53.9 

45 

28.0 

82.41 

89.7 

58.48 

40.1 

89.  1 

8S.I 

0252 

83.3 

71.  09 

15.3 

55.0 

46 

28.9 

82.14 

91.3 

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413 

90.2 

810 

02.86 

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76.39 

16.5 

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47 

29.9 

91.07 

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59.06 

426 

91.  z 

87.0 

03.ZO 

864 

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17.8 

57.2 

49 

30.8 

83.40 

94,4 

59.35 

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92.3 

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03.54 

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76.91 

19.0 

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49 

31.8 

83.73 

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59.64 

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93.4 

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01.88 

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77.28 

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594 

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2/32.7 

384.06 

39975 

359.93 

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2199.9 

404.22 

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377.58 

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33.7 

84.33 

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04.56 

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84.71 

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60.51 

49.9 

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31.8 

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78.18 

24.0 

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60.81 

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97.8 

92.7 

05.24 

9.58 

78.47 

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63.9 

54 

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85.39 

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fl.4 

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93.7 

05.58 

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7877 

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65.0 

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37.5 

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05.3 

61.39 

52.7 

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94.6 

05.92 

98.9 

79.07 

277 

66.1 

56 

38.4 

86.05 

063 

61.68 

54.0 

01.  1 

95.6 

06.27 

4100.4 

79.37 

28.9 

672- 

57 

39.4 

86.39 

094 

61.97 

55.2. 

OZ  1 

JM 

06.61 

02.0 

79.67 

30.1. 

68.3 

SS 

40.3 

8f.7/ 

fO.O 

62.26 

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03.2 

97.5 

06.95 

03.5 

79.96 

31.4 

69.5 

S9 

4/.3 

87.05 

11.6 

62.55 

S7.7 

04.3 

OS.  S 

07.29 

0511 

90.26 

32.6 

70.6 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


81 


42° 

45° 

/ 

T 

E 

c 

M 

X 

V 

T 

E 

C 

M 

X 

y 

2199.4 

40764 

4(06.6 

380.56 

39*?9 

J47/.T 

22570 

4zp.ro 

4-199.8 

399.68 

3907.6 

1539.2 

0 

22004 

0798 

08.  2 

80.86 

35.1 

728 

579 

z$.g$ 

4ZOI.4 

98.99 

08.8 

4-0.4 

1 

01.3 

08.  32 

09.8 

8I.[(, 

36.4 

7^.9 

59.9 

29.21 

02.9 

99.Z9 

IO.O 

415 

Z 

02? 

08.66 

/A* 

81.46 

376 

75.0 

59.9 

29.56 

04.5 

99.  60 

11.3 

427 

3 

03.2 

O90/ 

/2.9 

91.76 

3S.8 

76.Z 

60.  B 

29.  9) 

06.0 

99.91 

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43.3 

4 

04.2 

09.35 

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ff?.06 

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77.) 

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30.27 

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400.2  f 

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03.69 

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82.35 

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09.2 

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10.04 

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82.65 

425 

79.5 

63.7 

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383.55 

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432.04 

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475 

84.0 

676 

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10.9 

11.76 

25.3 

84  15 

487 

85.1 

695 

32.74 

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02.36 

222 

52.9 

12 

11.8 

12.  to 

26.9 

84.45 

50.0 

86* 

69.5 

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too 

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29.5 

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05.12 

33.1 

632 

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205 

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449 

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61.1 

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78.2 

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25" 

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37.73 

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06.66 

39.2 

69.9 

26 

25.3 

16.95 

48.6 

88*7 

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01.9 

83.o 

38.09 

41.7 

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464 

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26.2 

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50.2 

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68.4 

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38.44 

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38.90 

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29 

222ff./ 

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4246.3 

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29.  f 

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99.97 

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39.52 

479 

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74.7 

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30.  / 

18.  V) 

564 

90.18 

73.4. 

07.6 

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39.88 

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464 

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746 

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40.24 

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08.32 

47.6 

77.0 

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32.0 

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59.5 

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7S.8 

09.  8 

89.8 

40.5J 

52.5 

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48.9 

78.1 

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19.73 

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79.5 

13.2 

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41.67 

S7.2 

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525 

SIS 

37 

35.8 

2078 

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9/.99 

90.7 

(4.3 

93.6 

42.03 

587 

1037 

S3.7 

82.7 

38 

J6.8 

21.13 

67.3 

92.29 

91.9 

If.S 

94.  & 

42.39 

60.3 

io.es 

549 

83.8 

39 

2237.7 

4H.48 

4/68.8 

392.60 

3933  ^ 

1516.6 

22956 

442.75 

4261.3 

4J0.99 

3956./ 

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40 

3?.  7 

21.32 

704 

92.90 

84.4 

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96.5 

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59.7 

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97.5 

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750 

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88.1 

21.1 

99.4 

44.19 

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60.9 

896 

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42.5 

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94.11 

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621 

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633 

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94.72 

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301 

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336 

10.  I 

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85o 

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023 

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865 

1596 

75.3 

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952 

97.77 

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358 

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16.29 

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57 

55.0 

27.79 

967 

98.07 

Of  2 

370 

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49.25 

89.6 

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98.39 

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79.9 

06.9 

.59 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

44° 

45° 

T 

E 

c 

M 

X 

Y 

T 

E 

C 

M 

X 

Y 

0 

23/4.9 

449.9? 

A2.92.7 

4/7E/ 

J980.I 

)b08.l 

237:7.3 

472.08 

4-3853 

436J4 

405/.5 

167&.Z 

1 

If.  9 

J&.34- 

94.3 

17.52 

81.3 

09.2 

/#.? 

72.45 

£6.8 

36.46 

5E7 

79.4 

2 

/6.9 

SO.  70 

55.8 

/7.8) 

82.5 

/0.4 

7513 

72.83 

98.4 

-76.7* 

J3.8 

80.5 

3 

2* 

51.07 

97.4- 

19  15 

83.7 

//.  6 

7^.Z 

73  Zo 

89.9 

^7/0 

550 

917 

4 

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51.43 

98.9 

Hi.*, 

849 

12.7 

77.2 

73.57 

91.4 

37.42 

561 

829 

5 

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SI.  79 

4300.5 

18.77 

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13.9 

7£2 

73.95- 

93.0 

37.74 

57.4 

841 

6 

20.7 

52.  Ik 

02.0 

19.09 

873 

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79  Z 

74.-3Z 

945 

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585 

S5.3 

7 

21.7 

52.52 

035 

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sg.s 

tb.Z 

80.  ; 

74.70 

961 

38.38 

59.7 

96.4 

1 

22.7 

52.09 

03:  / 

13.71 

89.7 

17.4 

fttl 

75.07 

97.6 

38.7* 

60.9 

87.6 

9 

23.7 

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06.6 

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P2./ 

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99.  / 

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88.8 

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453.62 

4  30*.  2 

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275 

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ff.08 

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98.  1 

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88.0 

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084 

40% 

69.1 

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73.9 

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ZO 

2354  3 

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4323.6 

423.48 

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2352.8 

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4-416.1 

4-4254 

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170  /.g 

2f 

35.3 

57.64 

25.2 

23.79 

95.3 

32.5 

93.  8 

79.96 

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4287 

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392 

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10.1 

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42.  / 

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36.0 

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406 

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82.  6/ 

284 

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375 

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40.6 

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44.1 

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93.75 

330 

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44.0 

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2726 

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470 

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4"77P 

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37 

ft!  9 

63.  5} 

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28.84 

243 

5V.  2 

09.5 

86.0f 

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48  02 

94.8 

220 

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51.9 

63.90 

51.4 

29.15 

255 

52.7 

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86.40 

43.7 

40.34 

96.0 

23.2 

39 

52.8 

64.27 

52.9 

29.47 

26.7 

5-J.S 

//.r 

96.78 

45.3 

4867 

97.Z 

24.4 

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235J.S 

464.6^ 

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429.79 

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24-J24 

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448.99 

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41 

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65.0  / 

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48.3 

49.3/ 

99.5 

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55.7 

65.38 

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30.1 

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97.93 

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49.64 

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28.0 

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15.4 

88.31 

51.4 

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29.  Z 

44 

57.7 

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60.6 

31.06 

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59.4 

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88.69 

3-2.9 

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03.0 

30.4 

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58.7 

66.49 

62.1 

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33.9 

60.5 

174 

89.07 

54.5 

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46 

59.6 

66.86 

63.7 

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60.6 

67.24 

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32.01 

36.1 

629 

19.3 

89.83 

576 

51.2k 

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6/6 

67.6  / 

668 

32.32 

373 

64.1 

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5-9.1 

51.58 

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35.  / 

49 

62.6 

67.98 

68.3 

32.64 

38.5 

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51.90 

08.9 

36.3 

50 

23fc?.5 

468.55 

4369.9 

432.96 

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490.98 

4462.2 

452.23 

4-I/O.O 

1737.5 

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64.5 

68.72 

71.4 

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40.9 

676 

212 

91.3k 

63.7 

52.55 

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38.7 

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65.5 

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730 

33.60 

42.0 

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24.2 

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65.2 

52»? 

12.3 

39.9 

53 

66.5 

69.47 

74.5 

33.9J 

43.2 

69.9 

25.2 

9213 

66.8 

5320 

13-5 

41.1 

54 

674 

69.84 

760 

34.Z3 

44.4 

71.1 

26.2 

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68.3 

53.53 

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42.3 

55 

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70.21 

77.6 

J4.55 

45.6 

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272 

92.90 

69.g 

53.85 

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43.5 

56 

69.4 

7*>.W 

79.  / 

34.87 

46.8 

73.5 

2R2 

93.28 

71.4- 

541? 

16.9 

4-4.7 

57 

704 

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807 

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47.9 

74.6 

29.1 

93.66 

72.9 

54.50 

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59 

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82/2 

35.51 

49  / 

758 

3o.i 

94-05 

744 

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47-' 

59 

72.3 

7/.7(J^ 

837 

35  ?2 

503 

77.o 

31.1 

9443 

76.0 

55.15 

20.4 

48.3 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


46° 

47° 

/ 

T 

E 

c 

M 

X 

Y 

T 

E 

C 

IM 

X 

Y 

2432.1 

494.02 

4-4775 

4554-g 

4I2/.6 

17495 

249X.3 

5IV.-UD 

4-569.4 

475:22 

4-190.4 

/  822.0 

0 

33.J 

95!  20 

79.0 

55.  BO 

22.7 

50.7 

92  .5 

1859 

70.9 

7f.ff 

91.5 

23.3 

/ 

34-.I 

95.58 

90.b 

S6.I3 

23.9 

57.9 

937 

>8.99 

72.4- 

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TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


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TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


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43.9 

60.67 

01.8 

45.34 

33.9 

82.4) 

7 

79.9 

95.76 

SS.O 

39.64 

41.1 

21.92 

45.4 

61.03 

02.8 

•48.79 

35.4 

82.80 

8 

80.  9 

96.19 

S6.S 

40.00 

M..\ 

22.3fc 

469 

61.39 

03.8 

4-9.25 

36.9 

83.  17 

9 

268  /.  9 

59k.  62 

48S80 

5-403S 

2743  / 

622  .g  / 

49484 

5LI.7S 

2804.9 

649-70 

5032.4 

583.53 

10 

*2.9 

9705 

S9.S 

A0.70 

44-2 

23.ZS 

4-9.9 

62.11 

059 

50.  !(, 

39.9 

8/P0 

n 

84.0 

97.48 

6/.O 

41.06 

45.  Z 

23.69 

5V.  4- 

62.47 

06.9 

S0.6I 

4/.4 

84.27 

12 

8*.0 

97.91 

625 

4-1.4-1 

46.2 

24..I3 

52.9 

62.8? 

080 

51.07 

42.9 

84.6? 

13 

86.0 

98.34 

640 

4-176 

47-2 

H.S8 

54.4 

63/9 

09.0 

51.52 

44.4- 

£5.00 

14- 

£7.0 

38.77 

65.6 

42.  |Z 

*g.3 

25.02 

559 

63X5 

loo 

J7.98 

45.9 

83:37 

15 

880 

99.20 

67.1 

42.47 

49.3 

25.46 

574- 

63.91 

in 

52.43 

47.4 

a£7> 

ft. 

99.0 

99.64 

696 

42.83 

SO.  3 

2f.9/ 

/£9 

64.27 

/2.I 

-T2.89 

4-8.9 

86.10 

17 

9o.l 

600.07 

70.1 

43.18 

51.3 

Z6.?5 

604 

64.63 

/3.' 

5J.34 

50.4 

86.47 

'8 

91.1 

00.50 

7/.6 

43.53 

52.4 

26.80 

6/.9 

64.99 

/4.2 

53-80 

5/.9 

86.84 

/9 

2692' 

600.93 

4873.1 

543.89 

27S3.4 

6273* 

496*4 

565.35 

28/5.2. 

654.  as 

5053.4 

S87.20 

zo 

93  ( 

01.37 

74.6 

44.24- 

S4.4 

27.68 

64.9 

65.  71 

16  i 

54.7  1 

549 

87.57 

21 

94.1 

01.90 

76.1 

44.60 

55.  4 

29  13 

66.4 

66.07 

17.3 

55.  H 

5M 

87.94 

22 

951 

02.23 

77.6 

44.95 

Sfe.5 

28.57 

67.9 

66.43 

*3 

5J.62 

f7.9 

89.30 

23 

96  .i 

02.67 

79.1 

45.  3  / 

57.? 

29.02. 

69.4 

66.79 

*» 

56.  08 

59.3 

98.67 

24 

972 

0310 

806 

45.66 

58.5 

Z9.46 

709 

67/6 

2o.4 

56.54 

60.8 

89.04 

25 

98.2 

03  S) 

8ZI 

46.  OZ 

595 

29.91 

724 

67.52 

2/.4 

56.99 

62.3 

89  At 

26 

99.2. 

0*97 

837 

46  37 

60.6 

30.35 

73.9 

6788 

22.4- 

S7.45 

63.8 

89.78 

27 

2.700  i 

04.40 

85.2 

4673 

61.6 

30.80 

7f« 

£8.24- 

235 

57.  91 

653 

9o.l5 

28 

0/.3 

04.93 

86.7 

47.08 

62.6 

3/.2S 

76.9 

60-60 

24.5 

f8.37 

66.8 

90.51 

29 

2702.  3 

(,05.27 

4888.?. 

547.44- 

Z7637 

63A69 

44~794- 

56?-% 

-zgzs.6 

6SRW 

50683 

594*8 

30 

03.3 

Of.  70 

89.7 

47.79 

64.7 

32.  14 

79.9 

69.33 

266 

59.29 

69.8 

9/.2S 

31 

04.3 

Ok  14 

91.  Z 

48.  15 

tf.7 

32.59 

81.4 

69.69 

27.6 

S9.14 

7;.  3 

9/.62 

32 

OS.  3 

06.  57 

92.7 

48.  5V 

667 

33.03 

82.9 

70.05 

28.7 

bO.W 

72.8 

91.99 

33 

064 

07.01 

94.2 

4S.&6 

67.  8 

&?.4» 

84.4 

70.4-1 

29.7 

60.6(> 

743 

92.36 

34 

07.4- 

07.44. 

9ST.7 

49.22 

68.S 

3J.9J 

8F.9 

70.78 

30.7 

61.12 

7J-8 

92.73 

95 

08.4 

07.88 

972 

49.57 

69.8 

34.37 

87.4- 

71.14 

31.8 

61.  SB 

77.3 

97.10 

36 

09.4. 

08.32. 

38.7 

49.93 

70.9 

34.82 

899 

71.50 

32.8 

62.04 

79.8 

93.47 

37 

10.4 

Og.7f 

4900.2 

50.  Z9 

71.9 

35.27 

90.4 

7/86 

33.8 

62.50 

80.3 

9*84- 

38 

11.5 

09.19 

01-7 

50.64 

7Z.9 

35.72 

91.9 

72.23 

34.9 

62.96 

*/.g 

94.20 

39 

27/2.5 

605.62 

4-903.Z 

551.00 

277*9 

636.17 

4393.4 

572.59 

283S.9 

663.42 

50833 

594." 

40 

I3.S 

/o.ot, 

04.8 

57.36 

75.0 

36.61 

94.9 

72.95 

37.0 

63.88 

84.8 

^4.94 

41 

I4.S 

/O.SO 

06  3 

S-/.7I 

76.o 

37.06 

96.4 

73.3Z 

38.0 

64.34 

86.2 

95.3/ 

42 

IS.S 

#.93 

07.8 

52.07 

770 

37.SI 

979 

73.6% 

39.0 

64.80 

87.7 

95"  68 

43 

te.6 

//.37 

093 

52.43 

78.1 

97.9fe 

994 

7404 

4o.i 

65.26 

89.1 

96.05 

44 

/7k 

It.  SI 

108 

52.78 

79.1 

*4I 

5000°> 

74-.4-I 

4-1.1 

65.72 

9o.7 

96.42 

45 

/86 

X2.2S 

12.3 

S3.  14 

801 

3g.8t 

024- 

74.77 

4-2.1 

66  18 

92  Z 

36.79 

46 

'9.6 

/2.6g 

13.8 

53.50 

81.1 

39.  3  / 

03.9 

7S.I3 

43.2 

66.64 

93.7 

97.  Ho 

47 

20.6 

13.  IZ 

IS.  3 

J3.S5 

ffi.2 

39.76 

05.4 

75.50 

44.2 

67.  // 

95.Z. 

97.53 

48 

2/.7 

13.56 

16.9 

54.21 

83.1 

40.21 

06.9 

75.86 

45.3 

6757 

96.7 

9^9' 

49 

2722.7 

614.00 

49/8.3 

554  JT7 

Z784Z 

640.66 

50084 

576.23 

2846.3 

66R03 

S0982 

598.Z? 

50 

23.7 

/4  40- 

19.* 

54.93 

853 

41.11 

09.9 

76.59 

473 

68.49 

99.7 

98.65 

5"* 

24.7 

14.  ft 

11.3 

55.29 

86.3 

4/.SC 

H.4 

76.96 

48.4 

68.96 

5101.2 

99.02 

52 

25.7 

«iji 

22.8 

55.64 

87.3 

42.  0/ 

12.9 

77.32 

49.4 

69.42 

Oil 

9939 

53 

26.8 

IS.  7  5 

24? 

56.00 

98.4 

42.46 

144 

77.68 

50.5 

69.818 

04,2 

9976 

54- 

27.8 

16.19 

25.8 

56.36 

89.4 

4291 

1*9 

7805 

51.5 

7434 

057 

600./3 

53- 

28.8 

/663 

27.3 

5fe.72 

904 

4J.36 

t7.4 

78.4\ 

525 

70.81 

07.  / 

00.  59 

56 

29.8 

17.07 

Z*8 

57.09 

9/.4 

4J.S/ 

/8.9 

70.78 

53.fe 

7/.Z7 

08.6 

00.87 

57 

3o.<) 

17.51 

30.3 

57  A3 

92.5 

44.27 

204 

79.14 

54.6 

7X.74 

'O.I 

0/.25 

58 

31-9 

17.95 

31.8 

S7.79 

93.5 

4472 

21.9 

7951 

55.7 

72.  ZO 

tl-6 

0/.62 

59 

30 


TABLE    IT.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

53° 

5-^0 

JJ' 

T 

E 

c 

M 

T 

| 

C 

M 

T 

E 

C 

M 

o 

2W6.7 

672.66 

SI  13.1 

60/99 

Z9/9.4 

7<fc?.09 

5202.4- 

624  SO 

2982.7 

729.85 

529/5 

647.39 

1 

^"77 

73.  /J? 

14.6 

02.36 

20.  !T 

0/J6 

03.9 

24.87 

83.7 

30.34 

92.  8 

4777 

58.8 

7J.J9 

16.1 

01.73 

2/.5 

Of.  94 

054 

25.25 

34-8 

30.83 

943 

4S./6 

S9.8 

74.06 

17.6 

03.11 

ZZ.6 

02.  J2 

06.9 

25.63 

8S.9 

31.32 

95.  g 

4854 

60.9 

74.52 

19  1 

03.48 

?3.6 

^.79 

09.4 

26.0/ 

U.9 

31.91 

m 

48.93 

61.9 

7*39 

206 

03.85 

247 

03.27 

09% 

26.39 

99.0 

32.30 

99.7 

49.31 

62.9 

2T45 

22.) 

0422 

25.7 

03.  7  f 

113 

26.77 

99.0 

J2.79 

5300.2 

49.70 

64.o 

Zf.92 

236 

04.6o 

26.9 

04.13 

12% 

27/4- 

901 

3?.2* 

01.7 

50.08 

65.0 

76  ay 

250 

04.97 

27  S 

0471 

I4-.3 

2752 

9.1.1 

33.77 

03.1 

.50.47 

9 

66.1 

7*.  ar 

26.5 

05.34 

28.9 

05.18 

/J8 

2790 

92.2. 

34.26 

04.6 

50.86 

to 

Z€fc7./ 

677.32 

5-129.0 

605.71 

19299 

70S.  66 

52/7.* 

628.28 

2993.3 

77^.76 

5306.) 

65V.  24 

II 

6R2 

77.79 

29.5 

06.03 

31.0 

06.14 

19.7 

2*66 

94.3 

35.25 

07.6 

51.63 

11 

69.2 

70.25 

31.0 

0646 

32.0 

06.62 

20  Z 

29.04 

954 

3574 

O9.O 

52.01 

/3 

70.1 

79.72 

325 

06.83 

3*1 

07.  IO 

217 

23  4Z 

96.5 

3fe."23 

10.5 

52.40 

14 

71.3 

79.19 

34.0 

O7.ZI 

34-1 

07.58 

232 

29.90 

97.5 

36.72 

120 

52.7? 

IS 

7t3. 

79.65 

3515 

07.58 

35  z 

08.06 

24.7 

30  18 

9£6 

3Z2/ 

13.5 

53./7 

& 

73A 

90.12 

370 

07.95 

362 

08.54 

26.Z 

30.56 

99.6 

37.70 

15.0 

53.  5(, 

17 

7*.4 

90.59 

38S 

08.33 

373 

09.02 

276 

30.94 

3000.7 

J8.20 

16.4 

53.94 

IB 

7S.s 

91.  Of 

39.9 

08.70 

39.3 

09.50 

29./ 

31.32 

01.8 

^869 

17.9 

54.33 

/9 

765 

91.52 

41.4 

09.07 

39.4 

09.98 

70.6 

31.70 

02.8 

39.  18 

19.4 

5-4.72 

to 

V877.S 

C9/.99 

5142.9 

609.45 

2940.4 

7/046 

52321 

63208 

30039 

759.68 

5320.9 

655.  || 

21 

W 

82.46 

44.4- 

09.92 

41.5 

10.9  A 

33.6 

32.'46 

04.9 

40.  17 

223 

55.49 

22 

79.6 

82.93 

4r.9 

IO.ID 

41.5 

11.42 

35.  / 

JZ.84 

06.0 

40.67 

2.3.  g 

5/gg 

23 

S0.7 

83.40 

-474 

fO.57 

43.6 

11.90 

36  S 

33.22 

07.1 

41.16 

25.5 

55.27 

24 

81.7 

83.96 

4«.9 

M.94 

44.6 

I2.J9 

38.0 

33&\ 

OBJ 

41.65 

26.g 

5*.  65 

25 

9Z.8 

84.33 

504 

It.  32 

45.7 

/2.86 

39.  S 

33.99 

09.2 

42.15 

28.2 

57.04 

26 

93.8 

84.W 

51.9 

11.69 

46.7 

13.35 

41.0 

34.37 

10.3 

42.64 

29.7 

5743 

«7 

84.8 

8S.27 

Si* 

12.07 

478 

13.93 

42.5 

34.  7J 

II  -3 

43.14 

31.2 

57^2 

28 

95.9 

85.74 

54.9 

ttM 

4*9 

14.  31 

440 

35.fi 

12.4 

4-3.63 

72-7 

5820 

29 

86.9 

96.ZI 

S6.3 

/2.9Z 

49.9 

14.79 

4.5.4 

35.51 

'3.5 

44.13 

34.1 

.5*59 

30 

2899.0 

586*8 

51579 

613.19 

2957.0 

7X5-.28 

5246.9 

635.89 

30/4.5 

744.62 

5335.6 

658.98 

31 

89.0 

87.  if 

59.3 

13.57 

53.  0 

/J-76 

49.4 

36.27 

Jf.6 

45.  )2 

377 

59.37 

31 

9o.l 

97.6Z 

60.8 

1394 

53.1 

M.24 

49.9 

36.& 

/66 

45.61 

386 

f9.76 

33 

9l.l 

89.09 

62.3 

'4.32 

54.  » 

16.73 

51.4 

37.04 

17.7 

46.11 

40.0 

6o.l5 

34 

92.2 

98.37 

63.8 

14.69 

55.^ 

/7.2I 

52S 

37.42 

t93 

4661 

41.5 

60.53 

35 

33.  Z 

99.04 

65.3 

15.07 

56.2 

/769 

54.3 

37.90 

19* 

4710 

43.0 

66.92 

36 

94.3 

89.51 

66.7 

15.45 

57.3 

19  18 

55:8 

38.19 

209 

47.60 

445 

61.31 

?7 

9S.3 

89.98 

68.2 

»5g2 

583 

1966 

57.3 

30.57 

22.0 

49.09 

45.9 

61.70 

3* 

96.3 

90.45 

69.7 

I6.ZO 

554 

f9.i5 

S88 

39.95 

23.0 

49.  S9 

474 

6ztft 

39 

97.4 

90.92 

7A2 

16.57 

60.5 

/9.6J 

60.Z 

39.33 

Z4.I 

49.09 

48.9 

62.48 

40 

1898.4 

691.40 

5/72.7 

6/6.95 

2961.5 

720.12 

526/7 

6J97/ 

30152 

749.59 

5350.4 

662.97 

41 

99.S 

51.87 

74.7. 

/7.W 

62.6 

20.60 

63.'  2 

40.10 

26.2. 

fO.Og 

5  1.8 

63.25 

4i 

2900.5 

92.34 

7S.7 

17.70 

63.6 

Z\.O8 

64.7 

40.48 

27.3 

50.58 

S3.3 

63.64 

43 

0/.6 

92.91 

772 

/9o8 

64.7 

21.57 

66.2 

40.86 

28.4 

5109 

54.? 

64.03 

44 

02.6 

93.19 

78.6 

/ff.4S 

65.7 

22.  06 

676 

4/.Z5 

29.4 

51.58 

56.3 

64.4Z 

4S 

037 

93.76 

Vo.\ 

19.93 

66.9 

2254 

69.  / 

41-6? 

30.5 

52.08 

57-7 

64.81 

46 

04.  7 

^4.23 

8\k 

I9i\ 

679 

23.  03 

70.6 

4201 

31.6 

52.5? 

59.  Z 

65.ZO 

47 

05.9 

94.71 

93.1 

19.59 

6*9 

23.5/ 

72.1 

42.39 

X.6 

5307 

60.7 

65.59 

4* 

06.8 

95.18 

946 

19.96 

70.0 

24.00 

77.6 

42.7g 

*3.7 

5/57 

62.1 

65.98 

49 

079 

95.66 

?6.l 

20.34 

?l.o 

24.49 

75.0 

43.16 

34.8 

54.01 

63.6 

66.37 

5» 

7908.9 

696J? 

S'87.6 

620.72 

2972  | 

7*k97 

5276.5 

643.55 

3035.8 

754.S7 

5365T.J 

666.76 

r» 

/O.o 

96.6' 

^.0 

2/.09 

73.1 

25.46 

79.0 

A3.93 

36.9 

55.07 

66.6 

67  IS 

53 

11.0 

97.08 

90.5 

21.47 

74.2 

25.95 

79.  S 

4-43/ 

38.0 

55.57 

6g.O 

67.54 

SJ 

/Z.I 

97.58 

92.6 

21.  85 

75.1 

26.44 

81.0 

44.70 

39.  0 

5607 

695 

67.93 

54 

f3.l 

99.03 

93.5 

22.23 

7*.  3 

26.92 

9Z.4 

45.08 

40.1 

56.57 

71.0 

68.32 

55 

M* 

98.S/ 

95P 

22.60 

7Z4 

27  4^ 

83.9 

45.47 

41.1 

57.07 

72.5 

68.7/ 

5*6 

If.  2 

98.98 

96.5 

Z2.98 

7«4 

2790 

85.4 

45.85 

42.2. 

5757 

73.9 

69.  10 

S"7 

'6.3 

99.46 

980 

23.36 

79.5- 

2R39 

865 

46.23 

43.3 

58.08 

75.4 

69.50 

5* 

/?:3 

99.93 

994 

23.74 

805 

28.  98 

88.4 

46.62 

44.4 

58.58 

76.9 

69.89 

T<* 

/ff.4- 

700,4, 

52oo.9 

a»,it 

8/6 

?%v 

S?,? 

47,00 

45,4 

59.0  f 

78,3 

7C,2? 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


87 


5ff 

5^C 

58° 

/ 

T 

E 

c 

M 

T 

E 

C 

M 

T 

E 

C 

M 

304*5 

7f9f8 

5-379.8 

67067 

3//0.9 

790.08 

5^679 

($9^.33 

3/76/J 

9&.J7 

Sfff.6 

7/8.3Z 

0 

476 

6008 

F/.3 

77.06" 

12.0 

9(3.60 

694 

9473 

77/ 

i  (.90 

57.0 

/&  79 

/ 

486 

60.58 

82% 

7/4$ 

/3.1 

91.  ft 

70.9 

95.13 

70  1 

2242 

S85 

/9J9 

2 

49.7 

61.09 

84.  Z 

7t.9* 

14  2 

9/.63 

723 

95.53 

793 

22.95 

60.0 

/9.6o 

3 

50.  S 

61  59 

857 

72.D 

/53 

92.14 

7Jg 

95.93 

»A 

23.48 

61.4 

2o.oo 

4 

5J.9 

62.  09 

8/Z 

7S.63 

'6.3 

9^.(^ 

75.! 

96.33 

8/A 

24-  o; 

6Z3 

2o4/ 

5 

52.9 

6*.  60 

88.  (, 

73  oz 

/7>> 

?3.i7 

7«7 

%.72 

82? 

24.54 

64.3 

20.8' 

6 

54.0 

63./0 

90.1 

7).4\ 

/R5 

9*69 

7g.2 

97/Z 

83.6 

2507 

&.8 

ZI.ZZ 

7 

55.  1 

63.60 

9/.6 

7J.30 

/?6 

94z/ 

79.& 

97.5<? 

847 

i?5.60- 

67.2 

ZI.CZ 

8 

56.  1 

64.  // 

93.1 

74T.O 

20.7 

stt.7^ 

91.1 

9792 

85.8 

26.13 

68.7 

22.03 

9 

3057  Z 

764.6; 

53945 

674/9 

3121.7 

79524 

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474 

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TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


/ 

59° 

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61° 

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E 

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59  oo.  5 

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TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


62° 

63° 

64° 

, 

T 

E 

C 

M 

T 

E 

C 

M 

T 

E 

C 

M 

3442.7 

35475 

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8  '18.38 

351  1.  1 

990.24 

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88.9 

44.76 

81.4 

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13.4 

91.44 

90.3 

45.  19 

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279 

7/52 

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46./ 

56.50 

06.3 

19.67 

14.6 

92.04 

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285 

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to  5  3 

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4650 

861 

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59.26 

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95.01 

98.8 

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74.17 

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IZ 

575 

62.37 

20.5 

2397 

26.1 

9805 

059 

49.99 

95.4 

34.6 

90.9 

76.38 

/3 

58.6 

62.95 

ZZ.O 

24.40 

272 

99.65 

O7.4 

96.5 

35.3 

923 

76.9Z 

14- 

598 

63.54 

-Z3.4 

24.83 

08.8 

50.  86 

97.7 

359 

93.7 

IS 

6o.9 

64/3 

24.8 

25,26 

2*5 

9586 

IO.Z 

51.30 

998 

36.5 

9X1 

77.71 

/6 

62.0 

64.72 

26.2 

25.69 

30.7 

000.5- 

I/.6 

51.74 

3600.0 

37  1 

96.5 

79.15 

17 

63.Z 

65.3/ 

27.7 

26.  IZ 

01.  1 

13.0 

52.17 

37:7 

97.9 

78.60 

64.3 

65.89 

Z9.I 

26.55 

33.0 

01.7 

14.4 

52.6V 

OZ.3 

38.3 

99.J 

79.04 

19 

34654 

966.48 

5930.5 

726.90 

3534.1 

002.3 

60/5.9 

8-55.05 

3603.5 

10*9.0 

6100.7 

20 

66.6 

6707 

31.9 

2742 

353 

02.9 

17.3 

J3.49 

047 

39.6 

022 

79.93 

zl 

677 

67.66 

33.4 

27.85 

36.4 

03.5 

18.7 

53.92 

OS  8 

03.6 

8037 

22 

68.9 

68.25 

34.8 

29.28 

37.6 

04.  » 

20.  / 

54.36 

07.0 

SI 

os.o 

80.32 

23 

700 

68.5-4- 

36.2 

28.71 

38.7 

047 

54.80 

08  1 

4/.4 

06.4 

81.26 

24 

71.1 

69.43 

37.7 

29.  14- 

39.9 

05> 

2.3  O 

55.24 

09.3 

'42..I 

07.8 

81.70 

25 

72.3 

To.OZ 

39.  / 

41.0 

059 

244 

55.68 

/O.S 

92.15 

26 

73.4 

70.61 

40.5 

30.01 

06.5 

56.  M 

11.6 

43.3 

IO6> 

8259 

27 

74-h 

7/20 

4/.9 

30.44 

4*3 

07.  / 

272 

56.55 

43.9 

I2JO 

83.04 

7S.7 

7/.79 

4-J.4 

30.87 

44.5 

077 

2«6 

56.99 

l4.o 

44.5 

13.4 

83.48 

29 

3476.9 

972.39 

J-944.8 

83/.30 

3545fe 

J00A3 

603O.O 

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(,114.8 

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78.O 

72.98 

46.2 

31.74 

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5787 

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84.37 

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47.6 

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59.74 

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95.26 

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50.5 

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50.2 

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357 

59.18 

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477 

20.5 

8570 

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59.62 

2/0 

48.3 

2  1.9 

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15 

S3.  7 

75:94 

53.3 

3190 

52.5 

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J85 

60.06 

22.  / 

A-8.9 

233 

96.59 

36 

84.8 

76.53 

547 

34.33 

53.7 

IZ6 

400 

60.50 

23.3 

4-9.5 

24.7 

£704 

37 

86.0 

77/2 

56.2 

34.77 

54  £ 

/3.Z 

4-A4 

60.94 

245 

50.1 

2.6.1 

8749 

38 

87.  / 

77721 

576 

35.20 

56.0 

n.8 

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6/.3S 

25!6 

508 

27.5 

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39 

34  882 

97£3/ 

5959.0 

g9£63 

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1014.4 

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60.4 

36.07 

58.3 

15.0 

45.6 

62.Z6 

29.0 

52.0 

30.3 

88.92 

4/ 

905 

79.50 

61.9 

36.50 

59.5 

15.6 

47.0 

62.70 

29.1 

52.6 

31.8 

09.27 

42 

927 

80.10 

633 

36.93 

60.6 

I6.Z 

48.5 

63/4 

70.3 

33.2 

89.72 

0-3 

00.63 

64.7 

3737 

61.  ff 

16.8 

49.9 

63.58 

3/.5 

53.9 

34.6 

94/6 

44 

94.0 

fl.Z9 

66.1 

3780 

629 

17.4- 

51.3 

64.02 

32.6 

54? 

360 

90.61 

45 

9X1 

1.08 

676 

3F.23 

64  / 

19.1 

52.7 

64.46 

55.1 

374 

91.05 

46 

96/2. 

82.4% 

69.0 

.78.67 

65.2 

/8.7 

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64.90 

35.0 

F5"  S 

388 

91.50 

47 

974. 

93.07 

70.4 

39./0 

66.4 

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555 

65.  34 

56.4 

402 

97.95 

4-8 

9&S- 

83.67 

71.8 

39.54 

67-5" 

56.9 

6S.78 

373 

57  O 

4-1.6 

92.39 

49 

3495?  7 

984.2.7 

5973.3 

839.97 

3568.7 

lozo.s 

6058.4- 

866.22 

363  £5" 

1057.7 

6I4-3.O 

892.84 

50 

5500.8 

54.86 

74.7 

4040 

69.9 

21.1 

59.8 

6666 

39.7 

50.3 

44.4- 

93.29 

51 

02.0 

55.46 

76.1 

40.84 

ZI.7 

6/.2 

67/0 

4-0.8 

5P.9 

45-8 

93.73 

52 

03.1 

86.05 

77.  S 

4/.27 

72.2 

22.3 

626 

6754 

42..0 

59.5 

47-2 

94.18 

53 

04.3 

S6.65 

79.9 

4/.7/ 

73.3 

22.9 

64.0 

67.98 

43.2 

60  Z 

54.63 

54 

054 

872? 

80.4 

42.14 

74.5 

23.6 

65.4 

68.42 

44.3 

60.8 

500 

9507 

55 

066 

$7%5 

8/8 

42.58 

7.5.6 

24^ 

668 

68.87 

455 

61.4- 

51.5 

9552 

56 

077 

88.45 

83.2 

AJ.OI 

76.8 

24.8 

68.3 

69.  31 

46.7 

62.0 

529 

95.97 

57 

oag 

S3.  oA 

84.6 

AJ.45 

780 

69.7 

6975 

478 

627 

543 

96.42 

58 

IO.O 

89.64 

86.0 

43.88 

79  / 

ff.O 

71.1 

70.19 

4?0 

63.3 

5S.7 

96.86 

59 

Ill 


TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


, 

65° 

66° 

<o7° 

T 

E 

C 

M 

T 

E 

C 

M 

T 

E 

C 

M 

o 

3650.2 

10639 

6»57./ 

B97.il 

3720.9 

1/0*2 

6241.2. 

92436 

3792.4- 

;;  4-1.4 

6324.8 

951.78 

1 

5J.4 

64.6 

58.5 

9776 

22./ 

02.8 

426 

2482 

93.6 

42.0 

26.2. 

Sz  tA 

z 

52.5 

65.2 

59.9 

98.il 

23.2 

03.5 

44.0 

2527 

94.9 

42.7 

276 

52.70 

3 

53.7 

65.8 

61.3 

98.66 

244 

04.1 

45.4 

25.72 

96.0 

43.4 

29.0 

S3  16 

4 

54.9 

66.5 

62.7 

99.10 

25.6 

04.9 

46.8 

26.  18 

97.2 

44.0 

30.4 

53.62 

5 

56.1 

67.  1 

64.1 

99.55 

26.8 

05.4 

48.2 

447 

31.8 

54.08 

6 

57.2 

67.7 

9oo.oo 

29.0 

06.1 

4-9.6 

2709 

9ft  6 

453 

33.1 

5454 

7 

5£4 

68.3 

66.9 

00.45 

29.2 

06.7 

2754 

3900.8 

46.0 

34.5 

55.00 

8 

69.0 

68.3 

00.90 

30.4 

07.3 

52.4 

29.00 

02.0 

467 

35:9 

5546 

9 

60> 

69.6 

69.7 

01.35 

53.8 

28.45 

O3.2 

473 

373 

55.92 

/<? 

366/9 

1070.2 

6J7/.I 

901.80 

3772.7 

I/08.S, 

6255.2 

9*8.90 

39O4.4 

HO&0 

633S-.7 

956.39 

// 

63.  / 

70.9 

72.5 

02.24 

359 

O9.3 

56.5 

29.36 

OS  6 

AD  y 

40.1 

56.84 

/z. 

64.3 

71.5 

77.9 

02.69 

35.1 

09.9 

'   579 

of,  8 

49!  3 

41.5 

5730 

ij 

65.4 

72.1 

75.3 

Oi/4 

36.3 

10.6 

59.J 

30>7 

08.O 

50.0 

429 

57.76 

14- 

66.6 

72.8 

03.57 

37.5 

tl.2 

60.7 

30.72 

09.2 

5d7 

443 

58.23 

jf 

67.  9 

73.4 

"7$  1 

04.04 

38.7 

//•9 

62.  / 

3/  /$ 

/0.4 

5/.3 

45.6 

5?.69 

/6 

69.0 

74.0 

79.6 

04.49 

39.9 

12.5 

63.5 

31.64 

n.6 

52.0 

470 

59.  IS 

X7 

70.  / 

74-7 

81.0 

04.94 

13.2 

6A.9 

32.09 

12$ 

52.7 

4-8.4 

59.61 

J9 

71.3 

75.3 

05.39 

4-E  2 

13.$ 

66.3 

32.55 

14.0 

53.3 

49.8 

6007 

f9 

72.5 

75.9 

93.3 

05.84 

43.'4 

14.5 

67.7 

33.00 

IS.2 

54.0 

57? 

60.53 

20 

367?  7 

1076.6 

6185.2 

906.29 

3744.6 

IH5.I 

6269.1 

93*46 

3316.4 

1154.7 

6352.6 

960.99 

tt 

74\? 

772 

86.6 

4-5.8 

15.8 

70.5 

33.9; 

17.6 

55.3 

540 

61.46 

22 
2-3 

76.0 
77.2 

778 
78.5 

88.0 
89.4 

07.  13 
07.64 

4-7.0 
48.2 

16.4 
17  / 

71.9 
73.3 

34.37 
34.93 

18.9 
2O.O 

56.0 
56.7 

55:4 
56.7 

6  1.32 
6238 

2.4- 

78.4 

79.  1 

Og.09 

49.4 

17.7 

747 

?52S 

21  2 

573 

58.  / 

62.84 

25 

79-i 

79.8 

922. 

<?8.54 

50.6 

19.4 

76.1 

35.74 

22.4 

58.0 

59.5 

63.3/ 

X6 

80.7 

-90.4 

t~£ 

08.99 

51.8 

19.0 

77.5 

36.20 

23.6 

587 

609 

63.77 

27 

91.9 

81.0 

Q 

09.44 

52.9 

19.7 

78.9 

36.65 

248 

593 

623 

64.23 

2* 

83.1 

91.7 

A. 

09.83 

.54.1 

203 

80.3 

37  // 

26.0 

600 

63.7 

64.69 

29 

84.3 

81.3 

37.9 

/0.34 

2/.0 

817 

3757 

272 

60.7 

65./6 

30 

3685* 

IOdZ.9 

6/99.2 

9/0.79 

3756.5 

//2/.7 

6283.1 

938.02 

38284 

//6V.  3 

6366.4 

94562 

3/ 

86.6 

83.6 

6200.6 

1  1.2.4 

577 

22.3 

84.5 

38.48 

29.6 

62.0 

678 

66.08 

32 

875 

94-.Z 

02.O 

//.  69 

58.9 

aj.o 

85.8 

3894 

30.8 

627 

69.2 

66.55 

33 

89.0 

84.9 

OJ.4 

60.  / 

2*6 

39.39 

32.0 

(,3.4 

70.6 

67.0/ 

34 

85.5 

04.8 

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61.  3 

24.3 

88.6 

39.  85 

33.3 

64.0 

72.0 

6747 

35 

9/.3 

86.1 

06.2 

62.5 

24.9 

900 

403) 

34.5 

647 

73-4 

67.94 

36 

92.5 

86.8 

07.6 

13.50 

25"6 

9/4 

40.77 

35.7 

654 

74.0 

68.40 

37 

93.7 

<874 

09.0 

13.95 

649 

26.2 

92.8 

41.22 

36.9 

66.0 

76./ 

68.86 

39 

94.9 

89.0 

10.4 

1440 

66.1 

942 

41.69 

38.  / 

66.7 

77.5 

69.33 

39 

96.0 

88.7 

11-9 

I4-.85 

67.3 

27:5 

956 

42.14 

39.3 

67.4 

7«9 

6979 

4o 

36972 

1089.3 

6213.2 

9/5.30 

3769.5 

1128.2 

6297^ 

942.60 

3840.5 

1160.1 

6380.3 

97026 

41 

984- 

90.0 

146 

;5.76 

69.6 

28.9 

98.4 

43.06 

41.7 

68.7 

81.7 

70.72 

42 

99.6 

90.6 

16.0 

/6.2/ 

70.9 

29.5 

99.8 

43.51 

4-2.9 

69.4 

83.  / 

71-18 

4-3 

3700.? 

9).  2- 

17.4- 

16.66 

720 

30.1 

630  1  2. 

43.97 

44.1 

70.1 

24.5 

77.65 

44 

O2  p 

91.9 

'89 

17.)  1 

73.2 

Bo  8 

02.6 

4-4-  -fc 

45.3 

70.7 

85.8 

72:)l 

45 

03.; 

92.5 

202 

17.56 

74.4 

3l  5 

03.9 

4459 

465 

71.4 

87.2 

72.58 

04.3 

93.2 

2/.6 

75.6 

32.1 

45  JS 

47.7 

72.1 

88.6 

73.04 

47 

OJ.5 

93.8 

23  JO 

/8.47 

76.9 

32.8 

06.7 

45.80 

49.0 

72.8 

9o.O 

73.51 

49 

06.7 

94.5 

•244 

IB.9Z 

33.5 

08.1 

A6  Zk 

S0.2 

73.4- 

91.4 

73.97 

49 

07.9 

95.1 

252 

19.37 

7*2 

34.1 

09.5 

4672 

57.4 

74.  1 

92.8 

7444. 

SO 

3709.0 

I09S.7 

62272 

9/9.93 

3780.4 

1134.8 

63/09 

947/8 

3852.6 

1174:9 

63941 

974-.W 

sv 

/0.2 

96.4 

28-6 

2028 

35.4 

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47.64 

53.8 

7S-.5 

95.5 

7537 

1 

11.4 
tZ.6 

97.0 
977 

30.0 
3/.4- 

2073 
21.19 

8& 
84.0 

36.  \ 
36.8 

13.7 

4-8.10 
48.56 

55.0 
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76.1 
76.8 

96.9 
98.3 

75.93 

76.30 

li.9 

983 

J2.8 

ZI.64 

95.2 

37.4 

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49.02 

574 

77.5 

99.7 

76.76 

55 

15.0 

99.0 

34-.* 

22.09 

#64 

38.  1 

17.9 

4-9.48 

586 

78.2. 

640/.0 

7723 

56 

99.6 

35.6 

22.55 

876 

38.7 

19.2. 

49.94 

59.8 

78* 

02.4 

7769 

S7 

173 

IIO0.2 

370 

23-00 

88.8 

39.4 

20.6 

50.40 

61.1 

79.5 

03.8 

78.16 

58 

fo 

009 

38.4 

23.4! 

90.0 

4o.  / 

2Z.O 

50.8t 

62.3 

80.Z 

05.2 

7&62 

59 

197 

Ql-5 

39,  ff 

9l-2 

40.7 

23.4 

5/-32 

as 

30.9 

O6.6 

79.O9 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


-11 


<o8°             \ 

69° 

70° 

/ 

T 

E 

c 

M 

T 

E 

C 

M 

T 

E 

C 

M 

3864.7 
659 

//9/.6 
8ZZ 

6408.0 
09.3 

979  56,1 
80.O2 

39379 
39.  1 

21Z.7 
23.4 

6490.6 

92.0 

IOO7.7 
08.2 

40//.3 
I3.Z 

26?.o 
65.7 

6572.8 
74.2 

O36."2- 
36.7 

O 
1 

67.1 

829 

/0.7 

90.49 

40.3 

•24.1 

93.4 

08.6 

14.4 

66?? 

75.5 

37.2 

z 

68.3 

83.6 

12.} 

80.95 

41.6 

24.? 

947 

09.1 

I5-.7 

67  / 

76.9 

376 

3 

69.5 

84.3 

13.5 

8A42 

428 

ZS5 

96.1 

09.6 

16.9 

67  g 

78.2 

3ZI 

4 

70.9 

85.0 

14.9 

8/.S9 

440 

?6.2 

97.5 

/O.I 

18.2 

68.  5 

79.6 

38.6 

S 

72.0 

85.6 

16.2 

9235 

45.2 

26.9 

98.9 

IO.S 

19.4 

69.2 

B/.o 

39.  / 

t> 

73,2 

86.3 

17.6 

82.  83 

465 

27.6 

6500.  2 

11.0 

20.6 

70.0 

82.3 

39.5 

7 

74.4 

Z7.0 

19.0 

83.29 

47.7 

Z8.3 

01.6 

US 

z».9 

70.7 

83.7 

40.0 

9 

7S.(, 

87.7 

20.4 

£3.75 

48.9 

29.0 

O3.0 

11.9 

23.1 

7/4 

857 

40.5 

9 

387$  8 

//884 

642  1.9 

904.22 

39502 

229.7 

6504.3 

0/24 

4-024.4 

272  1 

6586.4 

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to 

78.0 

89.0 

23.2 

84.69 

SI.  4 

304 

05.7 

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Z5.6 

72  £ 

87.  8 

US' 

II 

79.3 

89.7 

245 

gfl5 

52.6 

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07.1 

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26.9 

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89.2. 

41.9 

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30.5 

90  A 

25.9 

85.62 

5*9 

319 

085 

13.8 

WJ 

74.2 

90.5 

42.4 

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817 

91.  / 

273 

86.09 

55.  1 

32.  5 

09-8 

t4-.3 

29.4- 

750 

9/9 

42.9 

14 

829 

91.8 

287 

3656 

56.3 

33.Z 

11.1 

14.8 

J0.6 

75.7 

93.2. 

43.4 

IS 

84-1 

924- 

300 

8702 

575 

33.9 

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15.3 

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76.4 

94.6 

4-3.9 

16 

853 

93.1 

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£749 

58.8 

34.6 

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15.7 

33.  / 

77.1 

96.0 

44.3 

17 

866 

938 

32  g 

£796 

60.0 

353 

15.3 

te.z 

34-.3 

77.8 

97.3 

44.8 

18 

078 

94.5 

342 

S&4-3 

6J.2 

56.0 

16.7 

/6.7 

?5.6 

785 

987 

4-5.3 

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3889.0 

1195.2 

64356 

90F.89 

3962.5 

1236.7 

65/9.1 

/0/72 

40J6.? 

IZ79.3 

6600.  / 

1045.9 

20 

10.1 

95.9 

369 

09.36 

63.7 

37.4 

194- 

17.6 

3ft  / 

So.o 

0/.4 

46.3 

Zl 

9  /.4 

96.5 

383 

89.83 

64-9 

38.1 

20.8 

>8.t 

39.3 

80.7 

O28 

46.7 

22 

926 

972 

397 

90.30 

66.2 

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222 

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81  A 

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93.9 

97.9 

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674 

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24 

95".  / 

90.6 

425 

91  & 

69.6 

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25 

96.3 

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91.70 

69.9 

40.9 

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44.3 

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975 

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45.2 

92/7 

71.1 

4-1.6 

277 

20.5 

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843 

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27 

38.7 

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466 

9264 

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42.3 

29.0 

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46.5 

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49.6 

28 

390  o.o 

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73.6 

43.0 

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IZ86.S 

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30 

02.4 

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94.05 

76.0 

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22.4 

50.6 

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15-0 

57.  / 

31 

03.6 

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52.1 

94.52 

77.3 

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34.5 

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879 

16.4 

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32 

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535 

9499 

78.5 

45? 

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372 

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95.93 

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35 

08  S 

06.  / 

57.6 

96.40 

82.2 

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24-.  8 

56.8 

90.8 

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53.5 

36 

09.7 

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96.87 

03.4 

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4-1.3 

25.2 

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37 

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97.34 

84.7 

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59.3 

92.Z 

24.6 

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38 

12.2 

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97.81 

85.9 

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4-4.  / 

26.2 

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39 

3313.4 

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6463.1 

998.18 

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1250.8 

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4461.8 

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14.6 

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98.75 

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89.6 

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656 

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11.7 

60.6 

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2-86 

66.8 

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32.7 

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44 

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12.4 

70.0 

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54.3 

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2.9.0 

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45 

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550 

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69.3 

98.0 

35.4 

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72.8 

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70.6 

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564 

30.5 

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332 

59.3 

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244 

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02.5 

983 

571 

578 

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39.5 

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64-769 

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3999.5 

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6559.1 

10  3  1.4- 

44744 

13009 

6640.9 

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50 

268 

16  5 

783 

035 

4000.8 

58.6 

60.5 

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7JT6 

01.7 

42.2 

6o.7 

51 

291 

172 

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03.9 

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59.3 

619 

32.4 

76.9 

014 

43.6 

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52 

29.3 

17.9 

81.0 

044 

03.3 

60.0 

632 

329 

78.1 

03.1 

449 

6/7 

53 

305 

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924 

049 

045 

60.7 

64.6 

333 

79.4 

03.9 

463 

62.2 

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31.7 

193 

937 

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05.7 

61.4 

66.0 

33.8 

80.6 

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477 

62.6 

55 

33.0 

20.0 

95.1 

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6Z.I 

67? 

343 

81.9 

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4-9.0 

63.  » 

56 

34.2 

2o7 

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063 

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348 

83.1 

06.0 

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63.6 

57 

75.4 

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879 

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63.5 

70-1 

352 

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51.7 

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58 

36.7 

22o 

892 

072- 

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64.3 

7_/.4 

35.7 

S5.7 

07. 

S3.  1 

64,6 

59 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


, 

w 

72° 

7?° 

T 

E 

C 

M 

T 

E 

C 

M 

T 

E 

C 

M 

o 
1 

40*6.9 
88.i 

L3O8.2 
09.0 

55.8 

1065.1 
65".  5* 

4/62.8 
647 

53.3 

€?&.(> 
37.0 

1094-3 
94.8 

4Z397 
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1398.0 
99.8 

69/6.3 
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IIZ3.3 
24.3 

2 

89.4 

09.7 

572 

G6i0 

65.4 

547 

38.3 

423 

996 

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3 

9o.7 

/0.4 

58.5 

665 

66.7 

54.8 

39.7 

9517 

43.6 

14004 

20^3 

25/3 

4 

92.0 

//.2 

670 

67* 

4/o 

449 

o/7 

2/.6 

25.8 

f 

93.2 

6J.2 

675 

69.Z 

5<3 

42.3 

96.7 

4,6.2 

0/.9 

2J.O 

26.3 

6 

94.5 

62  6 

68.0 

705 

577 

43.7 

972 

47.5 

02.7 

24.3 

26.8 

7 

95.7 

13.4 

63.9 

71.8 

578 

45.0 

977 

48.8 

03.4 

25.6 

273 

8 
9 

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98.2 

14.  1 
14.8 

ss 

69.9 
69.4 

74.1 

586 
59.3 

47.7 

9*2 
987 

50.0 
51.3 

04.2 
05.0 

270 
2g.3 

3? 

10 

4099.5 

f5 

66690 

/069.9 

4l7Sf> 

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6749.1 

[099.1- 

4252.6 

14-057 

6829.6 

//28.8 

If 

4/008 

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70.4 

76.9 

60.8 

504 

997 

5/9 

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31.0 

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OZ.O 

17.0 

70.7 

70.9 

78.1 

616 

S/.8 

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55.2 

07.3 

32.3 

29.8 

ff 

03.3 

178 

72.1 

7/-4 

79.4 

623 

53.  / 

00  6 

08.0 

337 

30.? 

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04.5 

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73.4 

90.7 

63.  1 

545 

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578 

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15 

05.3 

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74*. 

72.3 

820 

63.8 

558 

01.6 

59.1 

09.6 

36.3 

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077 

20.0 

83.2 

64.6 

572 

OZ.I 

604 

fo.4 

37.7 

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08.3 

20.7 

775 

73.3 

845 

65.4 

58.5 

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//  / 

39.0 

323 

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19 

09.6 

22.2 

78.9 
80.2 

7?.  8 
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85.8 
877 

66.1 
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59.9 
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03"  / 
03.6 

63.0 
64.3 

li.9 
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40.3 
4.1.7 

32.8 
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20 

4//2./ 

/  322.9 

6681.6 

1074.8 

4/89.4 

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H04.I 

42656 

14-135 

6843.0 

X/^.8 

21 

23.6 

82.9 

89.6 

6g.4 

63!  9 

016 

669 

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44.4 

34.3 

22 

14.6 

24.4 

84.3 

757 

90.9 

69.  / 

05.1 

682 

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45.7 

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23 

76.* 

92.2 

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69.5 

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35.3 

n.z 

258 

970 

767 

93.5 

70.6 

679 

06.1 

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48.4 

35.9 

25 

18.4 

26.6 

88.3 

772 

94-.g 

7/4 

69.3 

06.5 

720 

/7  3 

497 

36.? 

19.7 

273 

89.7 

77.7 

960 

7tl 

70.6 

070 

7/3 

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5/-0 

3(£  £ 

27 

ZI.O 

28  .1 

91.0 

78.2 

973 

729 

720 

075 

74.6 

19.9 

52.4 

37.'? 

2? 

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2£8 

996 

73.7 

73.3 

08.0 

7£$ 

19.7 

53.7 

37.7 

29 

23.5 

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93.7 

79.1 

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74.4 

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20.4 

55.0 

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30 

4  »  24.8 

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66957 

1079.6 

420/.2 

1  375.2 

6776.0 

1109.0 

4278.5 

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68564 

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26.0 

3l.o 

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024 

7519 

77.3 

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577 

39.2 

32 

273 

31.3 

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78.7 

81.1 

2-2.g 

597 

39.7 

33 

20.6 

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99.2 

81.  1 

05.0 

77.5 

80.0 

10.5 

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235 

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29.8 

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81.6 

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3  A./ 

34.0 

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790 

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63.1 

41  2 

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32.4 

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088 

79.7 

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86.3 

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64.4 

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37 

3J.6 

04.6 

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12.5 

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26.6 

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O59 

83.S 

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27.4 

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39 

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429/5 

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29.8 

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40.0 

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84.3 

921 

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94  / 

30.5 

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43 

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42.5 

39.9 
40.7 

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14.0 

86.0 
86.4 

17.8 
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lil 

15.4- 
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967 

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43.8 
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86.9 
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20.4 
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96.1 
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98.0 
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76.4 
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87.9 
88.4 

230 
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88.1 
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79.1 
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47.2 
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44.4 

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6802.8 

ft/99 

43045 

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68837 

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281 

91  1 

04.2 

19.4 

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376 

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49.  Z 

fz 

52.7 

46.6 

24.8 

9o  4 

294 

91.9 

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19.9 

072 

39.4 

85.7 

49.7 

53 

53.9 

474 

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9o'.8 

307 

92.7 

06.9 

20.4 

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39.2 

87  / 

542 

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32.0 

93.5 

08.2 

20.9 

09.8 

399 

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BO.  7 

55 

565 

48.8 

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33.3 

94.2 

09.6 

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5/2 

577 

496 

30.2 

346 

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437 

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61  6 

51.8 

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149 

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53.2 

T. \l!f,E    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


43 


74° 

75° 

76° 

, 

r 

E- 

C 

M 

T 

B 

C 

M 

T 

E 

C 

M 

43/76 

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44-76.5 

154-1.4- 

70&.O 

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18.9 

45.4 

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54.3 

978 

93.2 

77.3 

84.5 

778 

tyZ.  Z 

56.4 

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1 

20.  2 

462 

990 

54.8 

99.2 

94.0 

7  8  6 

95.0 

79.2 

43.0 

57.7 

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2 

470 

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4400.5 

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80.5 

43.9 

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81.3 

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91.9 

44.7 

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030 

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96.4 

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83.2 

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172 

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342 

75.6 

48.2 

73.4 

24.  / 

274- 

03.9 

29.1 

73.9 

O6.2 

34.7 

39 

4*70.1 

1476.4 

6949.5 

//7*9 

4449.7 

/524.9 

70Z8.S 

1204+ 

4-5304 

1574.7 

7/075 

1235.2 

46 

-71.4 

77.2 

50.8 

74.4 

5"^  1 

25.7 

30.  / 

04:9 

3I.'8 

75.5 

08.8 

35.7 

72.1 

52.2 

74.9 

52.4 

26.6 

3/.4 

05.4 

33.1 

76.4 

10.  1 

36.3 

A? 

74.0 

78.8 

53.5 

75.4. 

53.7 

27.4 

32.7 

05.9 

34.5 

772 

11.4- 

36.8 

43 

7S.4 

79.6 

54.8 

75.9 

55.) 

28.2 

34.0 

06.4 

12-7 

37.3 

44 

76.7 

90.4 

56./ 

764- 

56.4 

Z9.0 

35.3 

06.9 

372 

Tf'9 

140 

378 

45 

81.2 

575 

76.9 

577 

29  8 

36.6 

074 

3S6 

79.7 

/5.3 

38.3 

46 

79.3 

82.0 

5?  8 

77.4 

59.  1 

30.7 

30.0 

O8.O 

39.9 

80.6 

38.8 

47 

80.6 

82.8 

60.1 

77.9 

604 

31.5 

39.3 

08-5 

AI.3 

91.4 

179 

39.4 

48 

82.0 

816 

6/.4 

78.4 

61.7 

32.3 

40.6 

09.O 

42.6 

82.3 

19.2 

39.9 

49 

43833 

1494.4 

6962.8 

1/78.9 

4463.1 

/533.I 

7O4-I9 

/2<725 

45440 

1583.1 

7/20.5" 

1240.4- 

50 

8*6 

95.1 

64.  f 

79.4 

6*4 

34.0 

43.2 

/o.o 

4-5.3 

840 

2/.8 

40.9 

SI 

8*9 

86.0 

654 

80  O 

€58 

348 

445 

/0.5 

4-67 

848 

231 

41.4- 

52 

973 

869 

66.7 

go  5 

67  'l 

35.6 

45.8 

//.o 

48'l 

85.7 

24.4 

41.9 

53 

88.6 

876 

680 

8l.o 

684 

36.4 

47.Z 

11.5 

49.4 

865 

-2.5.8 

42.5 

54 

§9.9 

884 

69.4 

81.5 

698 

773 

48.5 

IZ.\ 

So  8 

873 

27.1 

43.0 

ss 

9;.2 

89.2 

82.0 

71.1 

38.} 

12.6 

S2.I 

882 

284- 

43.5 

56 

92.5 

90.O 

72  O 

82.5 

72.5 

38.9 

si.i 

13  1 

53.5 

890 

29.7 

440 

5-7 

73.3 

830 

73.9 

39.7 

524 

/3.  6 

54.8 

89.9 

31.0 

4-45 

59 

95:2 

91.6 

74.7 

83,5 

7S,Z 

/4.I 

562 

90,7 

32.3 

4-5.1 

59 

TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


, 

77° 

76° 

79° 

T 

E 

C 

M 

T 

E 

C 

M 

T 

E 

C 

M 

o 

45576 

J59/.6 

7/33.6 

(24?  6 

4639.8 

1643.0 

7211.6 

\2769 

4723.2 

\69S.8 

72890 

1308.5 

; 

5*9 

92.4 

J4-.9 

46.1 

4).2 

43.9 

12.9 

77.4 

246 

96.7 

90.3 

09.0 

2 

Bo  3 

93.3 

362 

/!£,£> 

425 

44-g 

142 

779 

26.0 

976 

9/6 

09.6 

3 

6/.7 

94.1 

37.5 

47.' 

439 

45.6 

'5.5 

78.4 

274 

985 

929 

/O./ 

4 

63.0 

950 

388 

477 

453 

46? 

161 

79.0 

28.8 

994 

94.Z 

10.6 

S 

64.4 

95.9 

40.1 

48  2 

46.7 

474 

/8.0 

79.5 

30.2 

/700.Z 

95.4 

11.2 

£ 

65.7 

96.7 

4|.4 

48> 

48.1 

48.2 

t93 

90.0 

3/.6 

96.7 

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7 

67.  / 

975 

42.7 

49.2 

49.4 

49.  / 

20.6 

80.5 

33.0 

O2  O 

9SO 

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68.5 

99.4 

44.0 

49.7 

50.  8 

50.O 

2/9 

81.1 

54.4 

02.9 

993 

9 

698 

99.2 

45.3 

50.3 

52.2 

50.9 

23.2 

91.  6 

35.8 

03.5 

7300.6 

13.3 

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457A-2 

\60o  \ 

7/466 

>250.£ 

46536 

1651.7 

72245 

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4737.2 

1704.7 

7301.3 

1313.8 

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51  3 

55.0 

52.6 

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82.6 

38.6 

O56 

031 

143 

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73.9 

01.8 

49.2 

5  (.8 

56.4 

535 

27.  / 

83.2 

40.0 

06.5 

04.4 

149 

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7*3 

02.6 

50.5 

52.3 

577 

54.3 

28.4- 

83.7 

4/.4 

07.4- 

05.7 

154 

14 

76.6 

03.5 

5/.8 

52.9 

59.  / 

55.2 

29.7 

84.2 

42.8 

08.3 

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159 

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780 

043 

53.  / 

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605 

56.1 

31.0 

£4.8 

44.2 

09.2 

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16  S 

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744 

05.2 

54.4 

6/9 

57.0 

323 

85.3 

4-56 

10.  1 

03.6 

170 

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ffO.7 

06.0 

55.7 

54  4 

63.3 

57.8 

336 

85.8 

47.0 

11.0 

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175 

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06.9 

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54.9 

64.7 

58.7 

349 

86.3 

484 

11-9 

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19 

83.5 

077 

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66.1 

59-6 

362 

86.9 

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12.8 

18.6 

20 

45848 

1608.6 

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/  256.0 

46674- 

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7237.4 

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47572 

17/3.7 

7314-7 

13  1  9.1 

2» 

86.2 

09.4 

60.9 

56.5 

68.8 

6/-3 

38.7 

879 

52".6 

14.6 

16.0 

197 

22 

87.6 

10.3 

62.2 

70.2 

62.2 

4o.o 

88.4 

54.O 

15.5 

17.3 

20  2 

Z3 

11:1 

63.5 

575 

71.6 

63.1 

4-1.3 

89.0 

55.4 

164- 

18.6 

207 

24 

90.3 

I2.O 

648 

73.0 

64.0 

42.6 

895 

56.8 

17.3 

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2i3 

25 

91.7 

12  *) 

66.  1 

58.6 

74.4 

649 

43.9 

900 

50.3 

18.2 

2/.S 

93.1 

13.7 

674 

59.1 

75.8 

65.7 

45.2 

90.5 

59.7 

19.1 

22.4 

22.3 

27 

94.4 

14.6 

68.7 

596 

772 

66.6 

46.5 

91.1 

6/.I 

200 

237 

229 

28 

958 

15.4 

70.O 

60.  ( 

78.5 

675 

47.8 

91.6 

62.5 

209 

25.0 

Z3.4 

29 

97.2 

16.3 

7/3 

60.7 

79.9 

63.4 

49.1 

92.1 

63.9 

26.2 

23.9 

90 

459*5 

1617.1 

7/726 

1261.2 

46913 

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7250.4 

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47653 

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73275 

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31 

9*9 

18  0 

73.9 

61.7 

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70.  f 

51-7 

93.2 

667 

236 

28.9 

25.0 

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460  A3 

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75.2 

62.2 

71.0 

529 

93.7 

68.1 

245 

30.  / 

25.5 

33 

026 

/9.7 

76.5 

62.8 

85.5 

7/9 

54.2 

942 

69.5 

25.4 

31.4 

26  / 

34 

04.0 

20.6 

77.9 

63.3 

86.9 

55.5 

94.8 

70.9 

26.3 

32.6 

26".6 

35 

05.4 

2/4 

79.1 

63.8 

883 

736 

568 

953 

72.4 

27.2 

33.9 

27  / 

06.8 

22.3 

80.4 

64.3 

89.7 

74.5 

58.  1 

9S.8 

73.8 

352 

27.7 

37 

08.  1 

23.2 

8  1.7 

64.8 

91.1 

59.4- 

96.3 

7-5T2 

29.0 

365 

28  i 

38" 

09.5 

24.0 

83.0 

65.4 

92.4 

763 

60.7 

96.9 

76.6 

29.9 

379 

28.7 

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84.3 

65.9 

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772 

62.0 

974 

78.0 

308 

39.  1 

29.3 

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46/2.2 

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4695.2 

16781 

7263.3 

12979 

4-779.4 

1731.7 

7-3403 

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13.6 

26.6 

869 

66.9 

96.6 

79.9 

64.5 

98.5 

80.8 

32.6 

A  16 

Jo.  3 

4Z 

150 

275 

92.2 

675 

98.0 

79.8 

658 

99.0 

82.2 

335 

429 

30.9 

43 

164 

28.3 

89.5 

68.0 

99.4- 

80.7 

67/ 

99.5 

837 

344 

442 

31.4- 

44 

17.7 

29.2 

908 

68.5 

4700.3 

81.6 

68.4 

1300.0 

85.1 

35.3 

454 

31.9 

45 

30.O 

92  1 

69.0 

02.2 

92.5 

69.7 

00.6 

86.5 

36.Z 

467 

32.5 

46 

20.5 

30.9 

934 

69.5 

03.6 

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71.0 

01.1 

879 

37J 

48.0 

330 

47 

2/9 

31.8 

947 

70.1 

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f4.2 

72.3 

01.6 

89.3 

38.0 

493 

33.  5 

48 

23.2 

32.6 

96.0 

70.6 

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73.6 

02.2 

9o.7 

38.9 

50.6 

34.  1 

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246 

33.5 

973 

7  /.I 

07* 

860 

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02.7 

92.  / 

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34.6 

50 

46260 

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47092 

1  686.9 

7276.  / 

/  303.2 

47936 

174-0.9 

7353.  \ 

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27.4 

35.2 

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72.2 

87.8 

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41.7 

54.4 

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28.8 

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7201-2 

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887 

73.  7 

043 

964 

42.6 

55.7 

36.2 

5*3 

37.0 

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13.4 

89.6 

80.0 

978 

43.5 

570 

36.7 

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3/5 

378 

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8i.3 

05  3 

99.2 

582 

373 

55 

32.9 

387 

05.1 

745 

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91  3 

82.6 

05.9 

4800.7 

453 

59.5 

37  g 

S"6 

343 

396 

06.4 

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922 

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02.  l 

608 

383 

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35.6 

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04.9 

48.1 

633 

394 

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384 

422 

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76.4- 

949 

87.7 

O6.3 

64.6 

39.9 

TABLE    H.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


45 


80° 

81° 

3Z° 

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r 

E 

c 

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C 

M 

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435 

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f 

106 

51.7 

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965 

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ao.s 

065 

2 

IZ.O 

52.6 

69.7 

4-21 

979 

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460 

74.4 

85-  / 

65.  / 

2/.g 

07.1 

3 

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535 

71.0 

426 

954 

09.  / 

473 

75.0 

?66 

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07.6 

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723 

43  Z 

4900.  £ 

lo.o 

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TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


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TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


47 


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48 


TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


, 

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TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


92° 


94 


M 


M 


M 


59**2 
3SJD 
36.7 
J8.4 

4o.  / 
41.9 
43.6 

fi? 

488 


S.I 

55-.71 
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60.9 
62.7 
644 
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59679 
69.6 

7/.3 
73./ 
74.8 
76.6 
78.3 
80.0 
8/8 
83.5 


Z5I85 
19.7 


2J.5 
24.7 
26.0 
272 
28.5 
29.7 

2F3/.O 
335 

36.0 
372 
39.5 
39.7 
4-1.0 


25435 
44.7 
460 
472 
485 
497 
F7.0 
522 
535 
54.8 


8243  I 
44.3 
45.4 
46.6 

«.« 

50.1 

52.4 
535 

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5?0 

59^3 
60.S 

til 

65  f 


'749.5 
50. 1 
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57.9 
52.5 

53.7 

549 

/7555 


573 

III 


60.3 
60.9 


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697 
70.9 
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7-43 
7*5 
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5985TJ  2556P  927/8 


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n! 
s; 

99.2 


7*9 
SO.  I 

824 

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85f9 

87.^ 
88.2 


62.1 
62.7 


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65.7 
66.3 
66.9 

1767.5 

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8i 

70.5 
7t.l 
7/.7 
72.3 
72.9 


6002.7  25^ 
04.5 
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08P 

18 
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60202 
22> 

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272 
290 
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82.6 
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26/9.7  $335.2 


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546 
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4/4 

67.7 
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36.3 
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39JB 
40.9 
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935£0  /809.9 
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6/622 
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2677.6 
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76.9 
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87.4 
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09.2 
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iz.y 


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227 
239 
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245 
25.' I 
25.7 
26.3 
269 
275 

18*8.1 

1 
II 

3/8 
32.4 
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336 


155 


62/6.4  2724.5  £426.1 


Si 

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64.9 
660 
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68.3 

9369.4 
70.6 
7/7 
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7S:  7 
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774 
78.5 
79.7 


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2o.o 
2/.9 

1!? 

27^ 


32.8 


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I?I 

32.5 
33.9 

35.2 
36.5 


ntl 

778 


20. "i. 
20.8 

21.4 


78.2 
40.0 
4/.9 


473 

fif 


4^7.6 
4/-9 
43.2 


273 
284 

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30.6 
31.3 
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jfr 

40.8 
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1^ 
453 
464 
476 


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37.3 

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29 


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42.8 
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446 
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a? 


538 
545 

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TABLE    II.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


, 

9 

5° 

36° 

37° 

T 

E 

c 

M 

T 

E 

C 

M 

T 

E 

C. 

M 

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6252.8 

2757.  3 

8448.7 

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2833.2 

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29/73 

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1933.1 

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52.7 

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/8.7 

836 

337 

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56.5 

509 

60.0 

67  / 

3S.9 

/8,-i 

970 

90.0 

20.2 

847 

343 

3 

58.3 

fS") 

52.1 

606 

37.3 

J9.3 

976 

21.6 

34.9 

4 

60  1 

567 

53.2 

61.2 

709 

387 

20.4 

98.2 

93.9 

23.0 

S6.9 

35.6 

5 

62.0 

58.0 

54.3 

61.8 

727 

40.  / 

Z1.S 

989 

8S7 

2.4.4 

880 

362 

6 

63.8 

554 

74.6 

4'.  5 

22.6 

99.5 

97.6 

2.58 

89.1 

36.8 

7 

65.6 

60> 

S6.(, 

63  j 

765 

429 

2-37 

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995 

27.3 

902 

374 

8 

67.4 

62./ 

57.7 

63.7 

44.3 

24/8 

00.7 

9/4 

287 

9/3 

3B  \ 

9 

69.3 

63.4 

58.8 

64.3 

842 

45-J 

25.9 

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30.  / 

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397 

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// 

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2g  2 

02  G 

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74% 

67.5 

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66!  / 

858 

49.8 

29.3 

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957 

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76.6 

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526 

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04.4 

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373 

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7<7.4 

23.2 

56.2 

38 

22.1 

029 

9/.J 

346 

86.2 

58.2 

IQ  A 

488 

71-8 

24.3 

568 

39 

245 

04.3 

92.5 

82.8 

36.5 

87.6 

S9.3 

20.0 

50.7 

735 

575 

4? 

63263 
28> 

2805.6 
07.0 

£493.6 

1883.4 
840 

64394 

40  2 

Z989.0 
90.4 

8S60.4- 
61  5 

/920.6 

6552.6 
54.5 

2974.7 
76.  / 

9626.5 
276 

S87 

42 

30.0 

084- 

958 

846 

42.1 

91.9 

62.6 

2/  S 

56.5 

776 

2#.7 

59.4 

4-3 

31.9 

09  S 

969 

853 

44JO 

93  Z 

6^  7 

2Z.S 

5$  4 

79.0 

29.8 

60.0 

-44 

33.7 

//./ 

9£/ 

859 

459 

94.6 

64.8 

60.3 

80.5 

309 

60.6 

45 

356 

12  5 

99.2 

86.5 

47? 

961 

659 

137 

62.2 

8A9 

32.0 

6/2 

46 

37* 

13.9 

87.1 

49.7 

97.5 

67.0 

243 

64.2. 

834 

33.1 

6}.9 

47 

39.3 

/53 

0/4 

#77 

98.9 

68.1 

250 

66.  ' 

84  S 

34.2 

625 

48 

41.  / 

'6.6 

02.5 

88.3 

535 

2900.3 

69.?- 

256 

68.0 

S63 

35.3 

£3.1 

49 

4-3.0 

/8.o 

89.0 

55/4 

o/.7 

70.3 

26.Z 

70.0 

87f 

36.4 

63.7 

5"0 
S~l 

6344.? 

467 

22/9.4 
20.8 

8504:8 

1889.6 
90.2 

64572 
59.  / 

290JJ 
045 

72.6 

19268 
27.5 

657/9 
73.8 

Z989.Z 

90.7 

&375 
38.6 

1964.4 
65.0 

52 

48.6 

22.1 

07.0 

90.8 

6/0 

06.0 

73.7 

7S.7 

39.7 

65.6 

5-4 

|f 

2-35 

08.' 
09.1 

9/4- 

629 

64.8 

0/4- 
088 

74.8 

28.7 
29.3 

77.7 
79.6 

93.6 
95.0 

40.8 
4-1.9 

III 

55 

26? 

927 

/0.'2 

77.0 

29.9 

0/.5 

96.5 

4B.O 

67.5 

56 

ito 

277 

//.S 

93.3 

68.6 

H.6 

78.1 

30.6 

93.5 

979 

441 

68.1 

57 

57# 

29.0 

/2.fe 

93.9 

70.5 

13.0 

79.2. 

3A2. 

£,5~4' 

99.4 

452 

€8.8 

55 

304 

137 

945 

7Z4 

80.3 

31.8 

#7:3 

3000.9 

463 

69.4 

5? 

6;.  is 

3/.8 

I4S 

95-.  / 

AT.9 

8J.4 

32.4 

89.  3 

023 

4-7.3 

70.0 

T.UiLE    IT.— FUNCTIONS    OF    A    ONE-DEGREE    CURVE 


A 

T 

E 

C 

M 

ggo.  & 

6591.2 

30O38 

86494 

19707 

IO 

66/0.6 

18.4 

59.4 

77.0 

2.0 

30.1 

33.1 

70.3 

33.3 

30 

49.6 

47.9 

81.2 

89.6 

A/\ 

69.2 

6Z.8 

920 

95.9 

SO 

88.8 

77.7 

9702.9 

2002.2 

99°-   0 

67og.6 

92.7 

13.7 

08.5 

10 

28.4 

3107.7 

24.5 

14.9 

ZO 

48.  2 

229 

35.3 

30 

68.1 

381 

46  1 

27.6 

4O 

88.1 

S3  3 

56.9 

33.9 

SO 

6808.2 

68.7 

676 

40.3 

tocP-  o 

6828.3 

3184.1 

877F.3 

20467 

10 

48.5 

99.6 

99.0 

53.'  / 

zo 

68.8 

3Z  15.  / 

99.7 

&.S 

30 

40 

89.2 
6909.6 

30.9 
465 

99104 
Zl.o 

65.9 
72  3 

.  50 

30.  \ 

£2.3 

31.7 

787 

101°-   0 

50.6 

78.  / 

42.3 

10 

71.3 

941 

9l'.6 

ZO 

9Z.O 

33  to'.l 

6J.4- 

98.0 

30 

70IZ.7 

Z6.I 

74.0 

21045 

40 

33.6 

4*3 

84.5 

10.  9 

50 

54.5 

95.0 

17.4- 

102*    0 

7075.5 

33  74.9 

890S5 

2123  9 

10 

96.6 

91.2 

]6.O 

30.3 

20 

7/178 

34077 

26.5 

36.8 

30 

39.0 

24,3 

433 

40 

60.3 

40.9 

47.4 

49.8 

50 

8/.7 

57.6 

57.8 

56.3 

/03°-    0 

7203.2 

74.4 

681 

62.9 

10 

24.7 

31.3 

78.5 

ZO 

463 

3S08.Z 

88.9 

7T9 

30 

68.0 

25.2 

99.* 

825 

40 

89.8 

424 

9009.5 

89.0 

SO 

73  1/.  7 

59.6 

19.8 

9S.6 

(04*-  O 
10 

7333.6 
55.6 

3576.9 
94  -z- 

9030.1 
40.3 

2202.1 
08.7 

20 

778 

36  /  /  .7 

so.s 

IS.  3 

30 

99.9 

292 

6O7 

219 

40 
50 

7422.2 
44.6 

46.8 
64.5 

70.3 
811 

Z8S 
35.1 

/oyQ-  o 

67.0 

823 

91.3 

4-17 

/o 

89.6 

3700.1 

9/0/4 

48.3 

zo 

7//2.  2  • 

18.2 

II.S 

54.9 

30 

349 

36.2 

2/.6 

61.5 

40 

57-7 

54.4- 

31.7 

50 

80.5 

72.6 

41.8 

74.8 

/06«-  0 

to 

7603.ST 
26.6 

3791.0 
3809.  4 

9/S/.8 
61.8 

2Z9I.S 
88.1 

zo 

49.7 

27.9 

7/.8 

94.8 

30 

72.9 

46.5 

91.9 

230/4 

40 

96.3 

9/8 

O8  1 

SO 

7719.7 

840 

920/7 

148 

/O/-P    O 

43.2 

39029 

116 

21.5 

10 

66.8 

21.9 

21.5 

29.1 

Zo 

90.5 

40.9 

3/4 

349 

30 

78/4.3 

6O  ( 

4i.3 

41.7 

40 

38.1 

79.4 

Sf.l 

484 

SO 

6Z.I 

98.7 

6/0 

SS.l 

A 

T 

E 

C 

M 

toe*-  o1 

70861 

40181 

9270.8 

236/.S 

/o 

79/0.4 

37.9 

80.6 

68.6 

20 

34.6 

S7.4 

90.3 

7S.3 

3o 

59.0 

772 

9300  1 

82.1 

834 

97.1 

09.8 

889 

050 
109-    0 

#708.0 
32.7 

4117.0 
37.1 

/9.5 
29.2 

95.8 
2402.4 

/o 

574 

573 

389 

09.2 

Zo 

82.3 

775 

48.5 

/6.0 

30 

8(073 

979 

58.1 

iZ.8 

32.3 

42/84 

67.8 

29.6 

so 

S75 

39.0 

77.3 

364 

/A?9    O 

91828 

4259.7 

9387.0 

2443.3 

/O 

8Z08.2 

80.5 

96.5 

SO.I 

33.7 

43O/.4 

9406.0 

S6.9 

30 

59.3 

22.4- 

15.5 

63.8 

40 

85.O 

43.6 

ZS.O 

70.6 

so 

93/0.3 

64% 

34.5 

77.S 

///*    0 

36.7 

96.1 

43.9 

84.3 

to 

6Z7 

4407-6 

3*3  3 

91.2 

899 

29.2 

62.8 

98.  > 

3O 

84-15-1 

50.9 

72.; 

25049 

40 

4-1.5 

72.7 

8/.5 

11.9 

68.0 

94.6 

90.9 

18.8 

^/^0-  o 

94946 

4576.6 

35-00.2 

2S25.7 

10 

8521.3 

38  & 

09.5 

32.6 

20 

48.1 

61'.  1 

78.8 

?9.5 

3O 
40 

7S.O 
860Z.I 

93.4 
4606.0 

28.  1 
37.3 

US 

«  50 

29.3 

28.6 

46.5 

60.3 

113-    0 

56.6 

S/.3 

55.7 

672 

10 

84.0 

74.2 

,64.9 

74-3. 

20 

87//.S 

97.Z 

74-  / 

91.2 

30 

39.2 

4-720.3 

S3.'3 

88.1 

6TO 

43.6 

24 

95.1 

SO 

94.9 

66.9 

960/.S 

£602.1 

II4&-  o 

8822.9 

4790.4 

96/0.6 

2609-1 

to 

SI.O 

4914.1 

19.6 

16.1 

2.0 

79.3 

378 

287 

23.1 

30 

8907.7 

61.7 

37.7 

30.1 

4O 

363 

95.7 

46.7 

37.1 

so 

64.9 

4909.9 

55.7 

441 

/A?9-   0 
/O 

93.8 
90ZZ.7 

34-.I 

64.7 
73.6 

£\ 

zo 

51.7 

8s'.  1 

82.5 

65.2 

3O 

5007.9 

722. 

40 

91/0.3 

32.6 

9700.3 

79.3 

SO 

39.8 

57.6 

09.2 

86.3 

116**-   0 

9169.4 

5082.7 

97/8.0 

2693.4- 

99.1 

S/O7.  9 

£6.9 

2700.5" 

20 

9229.O 

33  3 

3S7 

07.5 

30 

59.0 

S8.8 

44.4 

/  A  f^ 

40 

09.2- 

94.5 

S3.  2 

2/7 

Qso 

93/9.5 

61.9 

)I7-    0 

49.9 

36.2 

70.7 

3579 

10 

805 

62.3 

79.4 

43.O 

zo 

9411.3 

886 

880 

50.  / 

3O 

42.2 

53I5O 

367 

57.3 

40 

73.2 

4-1.5 

9805:3 

64.4 

so 

9  f  04.4 

68.2 

13.9 

7/5 

52 


TABLE  III.— CORRECTIONS'  (TO   BE   ADDED) 


VALUE 
FDR  A 
PCVME 

DCGRFF     OF     CURVE 

VALUE 
FOR  A 

t°cwvi 

2° 

3° 

4° 

5° 

<0 

7° 

8° 

9° 

10° 

11° 

/2o 

13° 

100 

.00 

.00 

.00 

.01 

.01 

.01 

.01 

.01 

.01 

Ol 

.01 

.02 

too 

ZOO 

-00 

.01 

.01 

.01 

.01 

.02 

.02 

.01 

0) 

03 

03 

.03 

200 

3OO 

.01 

.01 

.01 

.02 

.02 

.03 

.03 

.03 

.04 

.04 

.05 

05 

300 

400 

.01 

.01 

.02 

02 

.03 

.03 

.04 

.05 

.05 

.06 

.06 

07 

400 

500 

.01 

.02 

.02 

.03 

.04 

.04- 

.05 

.06 

.06 

.07 

.OB 

.08 

500 

600 

.01 

.02 

.03 

O4 

.04- 

.05 

.06 

.07 

.08 

.08 

.09 

lo 

600 

700 

.01 

.02 

.'04 

05 

.06 

.07 

.08 

.09 

JO 

Jl 

JZ 

700 

800 

.02 

.03 

'04- 

.05 

06 

.07 

.08 

.09 

10 

Jl 

IZ 

.13 

Boo 

9OO 

.02 

.03 

.04 

.05 

.07 

.08 

.09 

.10 

Jl 

JZ 

J4 

.15 

900 

/OOO 

.02, 

.03 

.Of 

.06 

.07 

.09 

JO 

Jl 

.14 

.16 

/OOO 

1100 

.02. 

.04 

.05 

.07 

.08 

JO 

Jl 

JZ 

.14. 

.15 

.17 

J8 

I/OO 

/ZOO 

.02 

.04 

.06 

.07 

09 

JO 

JZ 

.14- 

.15" 

.17 

JS 

ZO 

/Zoo 

13  OO 

.02 

.04 

.06 

.08 

JO 

Jl 

J3 

.15 

J6 

J8 

.20 

.21 

/300 

lAOO 

.03 

.05 

.07 

.09 

JO 

JZ 

.14 

.16 

.19 

.19 

.Z/ 

.23 

1400 

1500 

.03 

.Of 

.07 

.09 

Jl 

J3 

iS 

J7 

J9 

.Zl 

.23 

.25 

1500 

/600 

.03 

.05 

.08 

JO 

JZ 

.14- 

16 

JS 

.20 

.22 

.24 

.26 

/6OO 

/700 

.03 

.06 

.08 

JO 

.13 

15 

'.17 

.zl 

.23 

.26 

.Z9 

1700 

I90O 

.03 

.06 

.09 

Jl 

.13 

'.16 

J8 

.20 

23 

.25 

.27 

.30 

/goo 

1900 

.04 

.06 

.09 

JZ 

.14 

.17 

.19 

.21 

'24 

.26 

Z9 

.31 

/9oo 

2000 

.04 

.07 

.10 

IZ 

.If 

J7 

.20 

.23 

.25 

.29 

.30 

.3-3 

zooo 

2/00 

.04 

.07 

JO 

.13 

16 

.18 

.-21 

.24 

.26 

.2.9 

.32 

.35 

ZIOO 

zzoo 

.04 

.07 

JO 

J3 

'.16 

19 

.Zi 

.25 

.23 

.30 

.33 

.36 

2200 

2.300 

.04- 

.08 

Jl 

.14 

.17 

'.20 

.23 

.26 

.29 

.32 

35 

.32 

£3oo 

2400 

.05 

.08 

Jl 

JS 

J8 

.21 

24 

.27 

.30 

.33 

".36 

.39 

24.00 

2500 

J0f 

.09 

JZ 

.15 

.19 

.22 

.25 

.28 

3\ 

.35 

.39 

.41 

2500 

2600 

rfS 

O9 

.IZ 

.16 

J9 

.23 

.26 

.29 

'33 

.36 

.39 

.43 

2600 

2700 

.05 

'.09 

.13 

.16 

.20 

.24 

.27 

.30 

.34 

.37 

41 

44 

2.700 

2800 

.05 

JO 

.13 

.17 

.21 

.24 

.28 

.3Z 

.35 

39 

42 

'46 

2900 

Z900 

.06 

.10 

.14 

.18 

.21 

.25 

.29 

.33 

.36 

.40 

44 

'.49 

Z9oo 

30OO 

.06 

JO 

.14 

J8 

.22 

.26 

.30 

.34- 

.38 

.42 

'.45 

.49 

3000 

-3  too 

.06 

II 

J5 

.19 

.23 

.27 

.31 

.35 

'.39 

43 

47 

.51 

3/00 

3200 

.06 

II 

•    15 

24 

.28 

.32 

.36 

.40 

.44 

.48 

53 

3200 

3300 

.06 

.11 

.16 

'.20 

.24 

.2.9 

.33 

.37 

.42 

.46 

50 

.54 

3300 

3400 

.06 

JZ 

.16 

.21 

.25 

3o 

.34 

.38 

.43 

.47 

52 

.56 

3400 

350O 

.07 

'  IZ 

.17 

.Zl 

.26 

30 

35 

.40 

44 

.49 

53 

.58 

3500 

3600 

.07 

JZ 

•17 

.22 

27 

yt 

.36 

.41 

.'45 

.50 

.55 

59 

3600 

3700 

.07 

.13 

.23 

'27 

~32 

37 

42 

47 

56 

.61 

3700 

3800 
3900 

.07 
.07 

'./3 

:!f 

'.24 

.28 
.29 

'% 

'.38 
.39 

43 
'.44 

>8 
49 

'1 

.58 

.62 
64 

3800 
390O 

4000 

.08 

.14 

'» 

.24 

.30 

.35 

4o 

.45 

.50 

.55 

'.61 

.66 

44  OO 

4100 

.08 

14 

20 

.25 

30 

36 

41 

46 

.52 

57 

.62 

67 

4/OO 

42  OO 

.08 

'.14 

.20 

.26 

'31 

.42 

'47 

.53 

'.58 

64 

-69 

4200 

4300 

.08 

.1? 

.20 

.26 

.3Z 

'37 

43 

.49 

54 

60 

65 

.71 

43OO 

-4400 

.08 

.15 

.27 

.33 

'.39 

44 

50 

.55 

.61 

67 

.72 

•44-OO 

4-50-0 

09 

.15 

2>| 

.27 

.33 

.39 

'45 

51 

.62 

68 

74 

4500 

4600 

.16 

.22 

.28 

.34 

.40 

'46 

.52 

'55? 

6-4 

7O 

76 

4600 

4700 

.09 

.16 

.22 

.29 

.35 

.4-1 

'47 

.5) 

'.59 

65 

7t 

77 

4700 

4800 

.09 

.16 

23. 

.29 

36 

.42. 

'4? 

.54- 

60 

67 

'73 

'.79 

4800 

4900 

.09 

•17 

.23 

.30 

.36 

.43 

49 

.55 

.62 

.68 

'74 

.81 

4300 

SOOO 

.10 

.17 

.30 

.37 

'.so 

.56 

.63 

.69 

'76 

.82 

5OOO 

5/00 

.10 

.17 

.24 

31 

.38 

.44 

5.; 

.5? 

64 

7t 

77 

.84 

5700 

52OO 

.10 

.25 

.32 

.52 

59 

.65 

'72 

79 

.85 

520O 

5300 

JO 

•IS 

25" 

.32 

'.39 

'.46 

53 

.60 

.67 

.73 

So 

.97 

5300 

5400 

JO 

•  18 

.26 

.33 

.40 

.47 

54 

61 

.68 

7_5~ 

'82 

.89 

5400 

5500 

.10 

.19 

.26 

.34 

4f 

.4» 

.55 

'.62 

.69 

'.76 

.83 

.90 

5500 

5600 

Jl 

.19 

.27 

.34 

'4| 

.49 

.56 

63 

70 

.78 

B5 

.92 

5600 

5700 

J9 

.27 

35 

.42 

.57 

.64 

7Z 

96 

.94 

5700 

1  1 

.20 

.28 

.35 

43 

51 

.SB 

65- 

73 

'Jo 

.88 

.95 

58OO 

5900 

'if 

.20 

•28 

.36 

.44 

'.51 

59 

'67 

74 

9Z 

.97 

5900 

6000 

•  11 

.20 

.29 

37 

.44 

,52 

.60 

',6? 

.76 

9? 

.91 

.99 

6000 

TABLE  III.— CORRECTIONS    (TO   BE  ADDED) 


VALUE 

DEGRE 

•e   o» 

"    Cul 

7VE 

VALUF 

FOR  A 
l°CWJVE 

£° 

3° 

4° 

5° 

6* 

7° 

#° 

9° 

}<f 

11° 

12? 

IJ° 

\°CMVl 

6/00 

fZ 

.21 

.29 

.37 

45 

S3 

6' 

.69 

.77 

fff 

.92 

1.00 

6/00 

6200 

.12. 

.21 

.30 

38 

46 

'.54 

.62 

70 

.78 

'.96 

.94 

6200 

6300 

/2 

.21 

.30 

38 

',47 

.ss 

.63 

'.71 

.79 

%7 

95 

l°04 

63oo 

6400 

J-z 

.22 

.30 

39 

'47 

56 

.64 

.72, 

.81 

*  89 

'.97 

l.os 

65OO 

/* 

22 

40 

Q.Q 

57 

65 

73 

.82 

'.90 

93 

107 

6Soo 

6600 

'.13 

.22 

'3< 

"40 

'49 

'57 

'.66 

.7? 

.83 

.91 

'l.oo 

1.09 

6600 

67  OO 

.13 

!?2 

'41 

."50 

.'58 

67 

.76 

.93 

I.OI 

A/0 

6700 

68  OO 

.13 

.23 

.32 

'41 

50 

.59 

'68 

.77 

'  $& 

.94 

1.03 

A/2 

6800 

69OO 

.13 

.23 

'42 

.5/ 

'69 

78 

'.87 

.96 

t.os 

A/3 

69oo 

7000 

.13 

.24 

.33 

43 

.52 

.61 

.70 

.79 

.88 

.97 

LOG 

A/5 

70OO 

7/00 

.13 

.24 

.34 

43 

.53 

.62 

71 

.90 

S9 

.98 

l.os 

U7 

7fOO 

72  OO 

14 

.34 

44 

53 

.63 

72 

.81 

91 

/.OO 

I.o9 

I/It 

720O 

rjoo 

'.14 

!25 

35 

>4 

'54 

64 

73 

.8i 

92 

l.ll 

i  zo 

73OO 

7400 

14 

.25 

.35 

.45 

55 

.64 

'.74 

.84 

.93 

1  03 

A/2 

A  22 

7400 

7500 

'.14 

.26 

.36 

.46 

.56 

.65 

75 

95 

.94 

f.o4- 

/  14 

A  23 

7500 

76OO 

I  A- 

.26 

.36 

46 

.66 

.76 

'.86 

.96 

A  05 

A/5 

/  ^5* 

7600 

7700 

'.15 

.26 

.37 

>7 

>7 

67 

77 

.87 

97 

A  07 

1-17 

A  26 

77OO 

7800 

15 

.27 

.37 

.58 

.68 

.78 

.88 

'.98 

1.08 

7800 

7SOO 

.'5 

.27 

.38 

'.48 

.58 

.69 

.79 

.99 

.99 

1.09 

A  20 

1.30 

7900 

8000 

.15 

.27 

.38 

.4-9 

.59 

.70 

.go 

.90 

/.// 

/.2I 

132 

8000 

8ZOO 

.16 

.28 

.39 

.50 

61 

7f 

.82 

.93 

103 

/.I4- 

IZ4 

/.35 

5200 

8400 

.16 

.29 

.40 

51 

.62 

'.73 

.95 

/.06 

/  J  (> 

i  27 

1.39 

840O 

8600 

.16 

29 

4; 

.52 

.64 

86 

.97 

/.og 

I./  9 

A  30 

1.41 

8600 

8800 

.17 

.'30 

'.4Z 

.54 

.65 

'.77 

88 

.99 

I.H 

A  22 

1.45 

9800 

9000 

.17 

.3/ 

.4-3 

.55 

.67 

.78 

'.90 

/.oz 

1.13 

A25 

1.36 

1.48 

9000 

9ZOO 

.IS 

.31 

.44 

.56 

.6* 

.80 

.92 

I.o4 

1.16 

I.2S 

/.39 

1.51 

9200 

9400 

19 

32 

.45 

.57 

70 

.82 

.94 

JO& 

1.30 

A  42 

/.55 

9400 

9<00 

'.IS 

!33 

.46 

.58 

.71 

.84 

.96 

i.08 

1  2  1 

/33 

/.45 

A  58 

9600 

9800 

.19 

.33 

.47 

.60 

.73 

.95 

.98 

l.u 

A23 

A  36 

A4£ 

A6/ 

9800 

14 

IS 

\<0 

Itf 

to 

22° 

24° 

26° 

28° 

30" 

35"' 

40' 

/OO 

O2 

oz 

.oz 

.oz 

.03 

.03 

.03 

.03 

.04 

•04 

04. 

.OS 

100 

200 

.04 

.04 

.04 

05 

.05 

.06 

.06 

o7 

.07 

.08 

>9 

.10 

ZOO 

30O 

.05 

.Ofe 

.06 

>7 

.08 

.08 

.09 

I/O 

.11 

,/2 

.13 

.IS 

200 

400 

.07 

og 

oS 

JO 

tZ 

13 

.14 

./5 

.  /n* 

2.1 

400 

500 

.09 

09 

.10 

'/  / 

.13 

'.14- 

.If 

'.17 

.18 

19 

.zz 

.26 

soo 

600 

/  / 

'II 

.'/*• 

.ts 

.n 

.IB 

2.O 

.21 

,23 

.27 

.31 

600 

700 

'iz 

.13 

'.14 

/6 

.'8 

.20 

.21 

.23 

.25 

27 

.31 

34> 

700 

?00 

'14 

.15 

.16 

*/o 

.20 

.22 

Z4 

.27 

.29 

.31 

.36 

'41 

800 

900 

.ik 

.18 

!2I 

.23 

25 

.28 

.35 

.40 

.46 

9oo 

IOOO 

.IS 

19 

.20 

.23 

.25 

.28 

.31 

.33 

36 

.38 

AS 

$1 

/ooo 

IIOO 

.19 

*2i 

22 

.25 

.34 

.36 

'39 

'49 

'.57 

//oo 

IZOO 

.21 

"2,3 

'2.4. 

.-27 

~30 

'34 

.37 

.4-0 

'.43 

A4> 

..'54 

.62 

/zoo 

13  OO 

;4oo 

.23 
.25 

.'25 
27 

>8 

!?2 

1 

ill 

4O 
'.43 

43 
47 

46 
'.50 

SO 
54 

.58 
.63 

.67 
72 

1300 
1400 

/500 

27 

.2? 

.30 

.34 

.4-Z. 

.46 

So 

.54 

.58 

.67 

.77 

ISOO 

1600 

3O 

32 

*4/ 

45 

.49 

53 

.57 

.61 

.72 

.82 

/6OO 

1700 

.3o 

.32 

34 

.'39 

.43 

AS 

.52 

'.56 

61 

65 

.76 

.97 

I7OO 

ISOO 

32. 

.34 

'.37 

46 

.50 

55 

.60 

.64 

.69 

fl 

.93 

1900 

1900 

.34 

36 

!43 

.4-8 

.58 

.63 

.68 

.73 

s 

.98 

1900 

2000 

.35 

3? 

4/ 

.46 

.5; 

.56 

.6; 

.6C 

7I 

.77 

.9o 

/.O) 

2.OOO 

ZJOO 

.37 

.'40 

43 

AS 

.53 

.59 

.64 

.70 

'.75 

.81 

.94 

l.oS 

2100 

azoo 

.39 

4Z 

.'45 

.56 

.62 

.67 

.73 

.79 

.99 

1.13 

22.00 

2300 

41 

.44 

47 

'.53 

.58 

.64 

.70 

76 

.82 

*$8 

1.0) 

1.19 

2300 

2400 

.41 

46 

.49 

.6/ 

.67 

80 

.96 

*02 

IZ4 

2500 

.47 

.51 

!57 

.64 

70 

'.76 

.S3 

.89 

'.96 

i.iz. 

1.29 

2-5OO 

2600 

.'46 

49 

.53 

.59 

.66 

73 

.So 

93 

/oo 

1.17 

1.34 

2600 

2700 

.48 

'51 

.55 

62 

.69 

'.76 

.83 

'.90 

.97 

io4 

i.z\ 

/  39 

2700 

2800 

.50 

.53 

.57 

.64 

71 

.78 

.8G 

93 

/.OO 

/or 

1.26 

1.44- 

2900 

.51 

.55 

.59 

.66 

'.74 

.gl 

.89 

.96 

1.04 

i.n 

A  30 

1.49 

2.900 

.vi 


TABLE  III.— CORRECTIONS   (TO  BE  ADDED) 


VALUE" 
FOR  A 

l°cu«ve 

DEGREE      Of       CURVF 

V/«J-or 
FOR  A 

I°CURVE 

14° 

\5° 

16° 

18° 

20° 

22° 

24° 

26° 

28C 

30° 

55° 

40° 

300O 

.53 

.57 

.61 

69 

.76 

.64 

92. 

.99 

1.07 

1.15 

1.35 

'.54 

3000 

3/oo 

.55 

.59 

.63 

'.71 

.79 

.87 

.95 

103 

l.ll 

1.19 

/.39 

I  60 

31  OO 

3200 

.57 

61 

65 

73 

.81 

.90 

.98 

1.06 

1.14 

'23 

A44 

1.65 

3200 

3300 

.58 

.63 

67 

'75 

84 

.92 

1.01 

/09 

1.18 

'27 

1-48 

I.7O 

3300 

3400 

60 

.65 

69 

'78 

.86 

.95 

104 

1.13 

l.il 

1.30 

1  53 

1.75 

3400 

BSoo 

62 

.66 

71 

'.90 

.89 

.98 

1-07 

!.!(, 

I.Zf 

1.34 

1.57 

!.8o 

35OO 

36  oo 

64 

.68 

.73 

.82 

.91 

l.ol 

I.IO 

1.19 

1.29 

1.38 

1.62 

1-85' 

3600 

3700 

6f 

7O 

.7S 

85 

.94 

1.04 

1.13 

1.23 

/.3i: 

1.42. 

1.66 

1-90 

370O 

3800 

'.67 

72 

.77 

.87 

.97 

I.Of, 

A/6 

1.^6 

'.36 

146 

1-71 

/.% 

3goo 

3900 

.69 

'.74 

.79 

.99 

.99 

1.09 

A/9 

/29 

/.39 

1.50 

I.7S 

2.01 

3900 

4000 

.71 

.76 

.81 

91 

1.02. 

m 

/2^ 

133 

/43 

\53 

ISO 

2.0k 

4OOO 

4-JOO 

.7} 

.78 

.93 

'94 

1.04 

1.  IS 

/.ZS 

/.3h 

/47 

157 

/.B4 

2.11 

4/oo 

4-2.00 

.74 

.80 

.95 

'.96 

1.07 

I.I'd 

1.28. 

1.39 

/.5o 

1.61 

W9 

2.16 

4200 

4-300 

.76 

.82 

.87 

.98 

1.09 

1.20 

1.31 

14) 

/.54 

AG5 

1.93 

2.2\ 

4-300 

4-400 

.78 

84 

89 

1.01 

/./2 

I.Z3 

1.15 

A46 

I.f7 

A69 

1.98 

2.26 

4400 

4-500 

.Bo 

.85 

.9' 

1.03 

1.14 

1.26 

1.3$ 

/.49 

1.61 

/.73 

202 

2  32 

4500 

4$00 

.81 

.87 

.93 

UDS 

1.17 

129 

141 

153 

'.64 

/-76 

2.06 

2.37 

46oo 

4700 

.83 

.89 

95 

1.07 

1.19 

1.32 

1.44 

1.56 

1.68 

1.90 

2.11 

2.42 

4700 

4300 

.95 

91 

.97 

I.IO 

1.22 

'.34 

1.47 

1.59 

1.72 

1.84 

2.)5 

247 

4gOO 

A$OO 

.37 

.93 

99 

\.\Z 

I.ZS 

1.37 

1.50 

t.62 

1.7* 

1.88 

2.20 

2.52- 

4900 

5000 

.9B 

95 

1.0  1 

M4 

1.17 

140 

1.53 

'.66 

179 

I.9Z 

2.24 

257 

5OOO 

5/00 

.90 

.97 

1.03 

1-17 

1.30 

143 

1.56 

1.69 

1.92 

1.96 

2.29 

262 

5100 

5200 

92 

.99 

1.05 

1.19 

1.32 

1.46 

1.59 

1.72 

'.86 

1.99 

2.33 

268 

52  OO 

S300 

'94 

1.0  1 

1.07 

1.21 

I.3S 

I.4-9, 

I.6Z 

1.76 

1.89 

203 

2.38 

273 

5300 

5400 

.'96 

1.03 

I.IO 

1.23 

137 

/.SI 

165 

'.79 

'93 

207 

2.42 

2.78 

5400 

5500 

.97 

1.04 

l.ll 

IZ6 

1.40 

154 

1.69 

ISZ 

1-97 

2JI 

2.47 

283 

5500 

5600 

.99 

1.06 

1.14 

*.z% 

141 

1.57 

171 

/.86 

2.00 

2.15 

2.5-1 

288 

5600 

5700 

l.oi 

t.o8 

1.16 

|.3o 

145 

1.60 

1.74 

1.89 

2.04 

2.19 

2.56 

23? 

5700 

5900 

103 

I./O 

U8 

1.33 

147 

1.62 

/77 

1.9*- 

2.07 

2.ZZ 

2.60 

2.99 

5800 

5900 

104 

f.12 

I.IO 

»35 

1.50 

I.6S 

A8P 

1.96 

2.// 

2.Z6 

2.65 

3.04 

5900 

6OOO 

1.06 

f/4 

I.Zt 

1.37 

\5i 

1.68 

1.93 

199 

214 

2.30 

2.69 

309 

60OO 

6/00 

1.09 

IJ6 

1-2.4- 

139 

I.SS 

1.71 

1.87 

2.02 

2J8 

2.34 

2.74 

3.14 

6/OO 

6200 

I.IO 

1.19 

'.26 

/.42 

1.58 

1.74 

1-90 

2.06 

2.22 

2.3g 

2.7F 

7/9 

62-00 

6300 

l.ll 

I.ZO 

1.18 

144 

1.60 

1.76 

/.93 

209 

2.25 

2.42 

2.83 

3.24 

6300 

6400 

1.13 

I.ZZ 

1.30 

146 

1.63 

1.79 

1.96 

2.12 

229 

2.4J 

2.87 

3.29 

64oo 

6500 

1.15 

/.Z3 

1.32 

1.48 

1.65 

1.82 

1.99 

2./6 

232 

2.49 

2.92 

?.35" 

65-00 

6600 

U7 

/.25 

134 

1.51 

1.68 

1.85- 

202 

2./9 

2.36 

2.53 

2.96 

3.40 

6600 

6/00 

U9 

1  2-7 

/.3G 

I.S3 

1.70 

/.88 

2.05 

2  22 

2.39 

2.57 

3.0  / 

3.45 

6700 

6800 

/.2.0 

/.29 

1.  38 

155 

1.73 

i.9o 

2.08 

2>r 

2.43 

2.61 

3.  Of 

J.50 

6800 

6900 

LIZ 

/.3I 

1.40 

1.58 

1.75 

193 

2-11 

2.29 

2.47 

2.65 

3  JO 

3.55 

6900 

700O 

1.24 

)3* 

1.42 

1.60 

178 

1.96 

2.14 

2.32 

2.50 

a.68 

?.I4 

3.60 

7OOO 

7IOO 

I.Z6 

/.35 

1.44 

1.62 

A  80 

1.99 

2.17 

2.35 

2.54 

2.7? 

3.19 

3.65 

7100 

72OO 

A  27 

/.37 

146 

1.64 

1.83 

202 

2.20 

2.39 

2.57 

2.76 

3.23 

3.7/ 

72-00 

7300 

1.29 

1.39 

1.49 

1.6-7 

/.8(, 

204 

2.23 

2.42 

2.6/ 

2.  SO 

3.28 

3.76 

7300 

7400 

'.31 

/4l 

1.50 

1.69 

1.8V 

2.07 

2.2C 

2.45 

2.6* 

2.84 

3.32 

3.81 

74OO 

7fOO 

A33 

/42 

1.5  1 

1-71 

1.91 

2/0 

2.29 

2.49 

2.68 

238 

337 

3.86 

7fOO 

7600 

A  34 

A44 

1.54 

1.74 

1.93 

2.13 

2.32 

252 

272 

2.91 

3.41 

3.91 

7600 

77OO 

/36 

/.*6 

1.56 

1.76 

1.96 

"216 

2..3S 

255 

275 

Z.9J 

3.46 

3.96 

7700 

7900 

/.38 

1.48 

1.58 

178 

'.98 

2.18 

2.39 

2.59 

2.79 

2.99 

3.50 

4.01 

•7800 

7900 

1.40 

1.50 

160 

1.80 

2.01 

2.21 

242 

2.62 

2.82 

3.03 

3.55 

4,07 

7900 

8000 

142 

152 

I.6Z 

1.83 

2.03 

Z.24 

245- 

2.65 

Z$6 

3.97 

3.59 

4.IZ 

8000 

8200 

1.45 

1.56 

1.66 

1.97 

2.08 

2.30 

2.SI 

272 

2.93 

3.14 

3.68 

4.22 

82OO 

84oo 

1-49 

1.60 

1.70 

1.92 

2.13 

2.35 

2.57 

2.79 

3.oo 

$21. 

3.77 

4.32 

34.OO 

8600 

1.52 

f.63 

1.74 

1.96 

2.19 

2.41 

2.63 

2.85- 

3.07 

3.30 

3.86 

4.43 

9600 

8800 

1.56 

1.67 

1.79 

2.01 

2.24 

2.44 

2.69 

2.92 

3.  IS 

3.37 

3.95 

4.53 

88OO 

9ooo 

1.59 

171 

AgJ 

2.06 

2.21 

2.52 

275 

2.9g 

3.22 

?45 

4-04 

4.63 

9ooo 

9200 

'.63 

I.7S 

'.87 

2.10 

2.3A 

2.5g 

2.81 

3.05 

3.29 

3.53 

4.13 

4.74 

9200 

9400 

/.66 

1-78 

1.91 

2.15 

2.39 

2.63 

2..S7 

3.12 

3.36 

3.60 

4.Z1 

4.84 

9400 

9600 

170 

1.82 

I9S 

2.19 

2.44 

2.69 

2.94 

3.18 

3.43 

3.68 

4-31 

494 

9600 

9800 

1.73 

'.96 

1.99 

2.24 

2.43 

2.74 

3.00 

3.25 

3.50 

3.76 

4.40 

5.O4 

9£oo 

TABLE  IV.— CURVES  DESIGNATED   BY   RADIUS 


r,r> 


RADIUS 

MULTIPLY  I°C. 
FUNCTIONS  8Y 

DEGREE 
OF-  CURVE 

5 

.000975 

10 

.00/74-5" 

15 

.0026/8 

20 

.003491 

25 

.004-363 

30 

.005-236 

35 

.006/09 

40 

.00698  1 

45 

.007854- 

50 

.008727 

55 

.009539 

60 

.0/O472 

65 

.01  1344 

70 

.01  22.17 

75 

.O/3O90 

80 

.0/3962 

85 

.0/4835 

90 

.015708 

95 

.016580 

/oo 

.O/  74  y  3 

/05 

.019326 

ItO 

.0/9/58 

115 

,O20O7/ 

120 

O£0944 

125 

°Q2.  \  3/£> 

130 

.022689 

135 

140 

'.024434 

145 

.025307 

ISO 

.026/80 

155 

.02  7O52 

37^38.3' 

160 

.027^25 

36-25.2 

165 

.02  875?  7 

35-  /6.8 

170 

.02967O 

34-  12  6 

175 

.0305-4-3 

33-  l?.i 

180 

.031415 

32-  /53 

185 

.032288 

31-21.6 

30  •  30.9 

'.  03  4-03  3 

29-429 

ZOO 

.034-306 

28-573 

205 
2/0 

.035779 
.03665/ 

28-/4.0 
27-32.9 

2/5 

.03757.4 

26-53.7 

220 

.038397 

26-  16.4 

£25- 

.039269 

25-  -40.8 

Z3O 

.04OI42 

25  -06.7 

235 

.04/O/5 

Z4-34./ 

2AO 

04/887 

24  -  O3.O 

245 

.042760 

23-33J 

250 

.04  363  3 

23-04.4 

255 

044505 

22  -369 

260 

!  04  53  78 

22  -  /0.'5 

265 

046250 

2/  -45M 

270 

.047/23 

21  -  20.6 

27T 

.047996 

20-57.1 

z  $o 

0A886  8 

20-344 

285 

04974  / 

2O-  12.5 

290 

'.05-06  14 

19-51.4 

295 

05/486 

'9-3/0 

3OO 

.052355 

>9  -  11.3 

RADIUS 

MULTIPLY  I°C. 
FUNCTIONS  BY 

DEGREE 
OF  CURVE 

305 

.053232 

18^  52.2 

3/0 

.054/04- 

18-33.9 

315 

054977 

18-16.0 

320 

!o55850 

I7-S8  7 

325 

.056722 

/7-4-2.0 

330 

.0575-95 

17-2.5.8 

335 

.0584-68 

17-  IO.O 

340 

.0*9340 

16-549 

345 

.0602/3 

16  -  40.0 

35-0 

.06/086 

355" 

.06/958 

16'  116 

360 

.06283/ 

15-58.0 

365 
370 

.063703 
.064576 

15-  32.0 

375 

.065449 

IS-  /95 

390 

.06632J 

1  5-  07.3 

J&5- 
390 

.067/94 
.068067 

14-55.4 

395- 

.068939 

J4'3ZJ 

400 

.0698/2 

14-21.7 

405 

O7OG8S 

W-II.O 

A-IO 

'.071*5  '7 

14  -  00.6 

4-15 

.072430 

/  3  -50.4 

420 
425 

.073303 
.074-I7S 

/3-40.5 

4-30 

.0750  4-8 

/3~2/  3 

435 

.075921 

/3-I2.0 

440 

.076793 

/3  *O3  O 

445 

.077666 

/2  -54.1- 

4-50 

.0785-39 

455- 

.0794-1  1 

/Z-  37.1 

46O 

.080284 

X2-28.8 

465 

.08I/S6 

I2.-20.7 

4-70 

.082029 

12-12.8 

475 

.082902 

/2  -05.  / 
//-575 

485 

'.08464-7 

!/-5o.\ 

4-90 
495 

.085520 
.086392 

50  Os 

.087265 

H-W.7 

SOS 

.088138 

//  -  2  1  9 

5/0 

.0890/O 

//  -  »5.2 

5/5 

.0£$883 

//  -  08.6 

520 

.090  7,56 

//  ~  02.1 

525 

09/628 

530 

.09250/ 

A3  -496 

535 

.093374 

xo-43.5 

545 

.094-246 
095//9 

/0  -  375 
/0-3/.7 

550 

'.  0959  9  2 

555- 

.096864- 

/O  -2O3 

560  - 
565 

.097737 
098609 

10-147 
IO-09.2. 

57O 
573- 

.099482 
.1003  55 

/0-03? 
9-58.6 

580 

./0/227 

9-535 

585 

./02,/cO 

9-48.4 

590 

./02973 

9-434 

595 

9  -  385 

6OO 

'.104718 

9-33.6 

TABLE  V.— RADII 


, 

DEGREE    OF    CURVE 

0° 

1° 

2° 

5° 

4° 

5° 

G° 

7° 

r3° 

9° 

0 

Infinite 

S729.65 

2864.93 

/9/G08 

143269 

1/46.28 

95537 

819.02 

71678 

63727 

3437747 

5635.72 

2841.26 

/899.S3 

1426.74" 

/1  4-2  .47 

952.72 

81708 

7/5.23 

636.10 

2 

7/887.3 

5544.83 

2817.97 

/  8  89.  09 

/420.85 

f  /  3^  69 

8/5.14 

7/381 

634.93 

3 

/  I4S9I.6 

5456  82 

2795.06 

187877 

/1  34.94 

94748 

8/3.22 

712  33 

633.76 

4 

85943.7 

5371.56 

2772.53 

/409.2I 

M3A2/ 

94488 

3//.30 

7/087 

632.60 

5 

68754.9 

5288-92 

2-750.  )5 

185847 

140)46 

1127.50 

94-229 

709.40 

6)1.44 

6 

572958 

5^08.79 

272852 

'848.48 

'397.76 

/I  £3.82 

939.72 

80750 

707.94 

630.29 

7 

49//07 

5131.05 

2707o4 

/83S.59 

1392.10 

H20./6 

937/6 

805.61 

70649 

629.14 

8 

4297/.S 

505X59 

2685.89 

</  16.52 

9J4.62 

801.73 

70505 

62799 

9 

38/97.2 

4982.33 

266508 

1819.14 

1380.92. 

932.09 

80/.86 

703.61 

62695 

10 

343775 

49M.IS 

264A.58 

/809.57 

1)75.40 

110933 

92957 

800.00 

702.18 

62571 

II 

3/2523 

4841.98 

£624.39 

1800.10 

/  105.  76 

92707 

738  14 

70075 

62459 

12. 

286479 

4774.74 

£604.51 

'790.73 

/3g449 

H02.2? 

9Z458 

79630 

69933 

623.45 

13 

264442 

4709.33 

2584.93 

I79I4S 

1)59.10 

1098.70 

922  10 

79446 

697.91 

62232 

14- 

24-555.4 

464569 

"2.  565  65" 

1772.27 

/  353.75 

1095.20 

9/9.64 

69650 

62  1.20 

IS 

2Z9I&3 

458/75 

2546:64 

/763.I8 

134845 

1091.73 

.9/7/9 

79081 

69509 

62009 

/6 

214859 

4523.44 

2527.92 

'754.19 

/  343  18 

IO  88.28 

9I4.7S 

789.00 

693.70 

618.97 

>7 

20222.1 

446470 

2509.47 

1  745.29 

'33796 

108495 

9/233 

787  20 

692.30 

617.87 

19098.6 

4407.46 

2491.29 

J332.77 

108144 

909.92 

78540 

69091 

61676 

'9 

18093.4 

4351.67 

2473.37 

1727.75 

1)27.63 

107805 

907.52 

783% 

689.  5  3 

615.66 

20 

17/58.8 

429728 

245570 

17/9.12 

X32253 

1074.69 

905)3 

78/84 

688.16 

6/456 

21 

/  63  70.2 

4244.23 

2438.29 

f  7IO.57 

1)17.46 

I07lf.34 

902.76 

780.07 

686.78 

613.47 

22 

/5626  / 

4192.47 

2421.12 

1702  10 

/JI243 

IO68.0I 

900.40 

779.  )l 

68542 

6/2.J8 

23 

/4946.S 

414196 

2404.19 

169172 

1)07.45 

I06A7I 

898.05 

776.55 

GftA  OL 

611.30 

24 

'4324.0 

4092.66 

238750 

/6S5.42. 

/302.50 

I06i43 

895.  7  7 

77481 

682.70 

6/021 

25 

/  37570 

4044.51 

Z37/.04 

K.77.2Q 

'058.IC 

893.39 

773.07 

£81.)  5 

609.14 

26 

/3222./ 

2354.80 

I6C906 

1232.71 

IO5492 

891.08 

77/.34 

&80.0I 

608.06 

27 

/27324 

3951.54 

Z3  38.78 

f  66  1.00 

'Z87.87 

I05/.70 

76961 

678.67 

(,06.99 

28 

/2  2  7  7/7 

390664 

2322.98 

/653.0I 

I2Z3.07 

/04849 

886.49 

767.^0 

677.34 

605.93 

29 

118543 

3862.74 

•2-307.39 

/645.H 

'278.30 

884.  Zl 

766.19 

676.01 

60486 

J0 

11459.2 

38198) 

229201 

X637.28 

/273.S7 

/O42  14 

881.95 

76449 

67469 

603.80 

31 

1  loS95 

377785 

Z  2  76.84 

1629.52 

/  268.87 

1039.00 

879.69 

762.80 

673.37 

602.75 

32 

I0743.O 

3736.79 

£261-86 

X62/.84 

/264.2I 

103587 

877.45 

67206 

601.70 

33 

10417.5 

369661 

224708 

1614.21 

'259.58 

103276 

875"  2.2. 

75943 

670.7S 

(,00.65 

34 

IOIII.I 

365729 

"2,232.  4Q 

1606.68 

X254.98 

1029.67 

873.00 

757.76 

669.45 

599.61 

35 

9822.18 

36/8.80 

221809 

/S99.2I 

'25042 

1026.60 

870.79 

7  56.  to 

668.  /5 

598.57 

36 

9549.34 

3581.10 

2203.87 

'$91-81 

/2  45.89 

1023  55 

86860 

754.44 

666.86 

597.53 

37 

929/.2S 

3*44  19 

2-189.84 

f  584  48 

/  24  1.40 

1020.51 

86641 

75-2.80 

€6557 

596.50 

38 

9046.75" 

3S00.02 

2175:98 

1577.2] 

10/7.49 

864.24 

757.  16 

664.29 

59547 

39 

88/4.78 

3472.59 

2162.30 

/57O.OI 

/2325I 

1014-50 

862.07 

74952 

663.01 

594.44 

40 
41 

8594.42 
8394.80 

343787 
3403.83 

214-8.79 
£13544 

156288 
'  5~5  5.  81 

/228.II 
/Z23.74 

loii.fi 

I008.5S 

859.92 
857J8 

74627 

661.74 
66047 

F93.42 
592.40 

42 

8'85.  16 

3370.46 

2/22'.26 

/54S.80 

1219.40 

/005.60 

744.66 

659.21 

591.  38 

43 

7994.81 

3)37.74 

2/09.24 

/54'-  86 

12.15.09 

IO0267 

85353 

743.06 

657.95 

44 

78/3.11 

3305.65 

2.096.39 

/5J4.9* 

I2.1O.92 

999.76 

851.'  41 

74/46 

656.69 

589.36 

45 

7639.43 

3274.17 

I20f>57 

996.87 

84932 

739.86 

65545 

58836 

46 

747/42 

3243.29 

207A/3 

/52j  4.9 

I20i  36 

99*99 

84723 

738.28 

654.20 

597:36 

47 

73/4.4; 

3212.98 

/5I470 

1198.17 

991.13 

845.15 

73670 

652.96 

586.36" 

48 

7/62.03 

3  '£3.23 

2046.48 

I$O80(> 

//940I 

988Z% 

843.08 

735.13 

65'.  73 

585.36 

49 

70/5.87 

3/54.03 

2034.37 

ISOIA8 

1/89.88 

985.45 

841.02 

733.56 

650.50 

5^4.37 

5o 

6875.55 

3/25.36 

•2.022.41 

1  494.9  S 

1185.78 

98264 

838.97 

73201 

649.27 

58338 

5-1 

6740.74 

309720 

2O  JO  51? 

JI8/.7/ 

979.84 

83693 

730.45 

64805 

582.40 

52 

6611.12 

3063.55 

'998.90 

1177.66 

977.06 

834.90 

728.9  / 

646.84 

581.42 

53 

64-86.38 

3042  39 

198735 

I475.7/ 

1  173.65 

974.29 

727.37 

64563 

580  4  i 

54 

6366.26 

3015.71 

'97S.93 

(44941 

1169.66 

97/.S4 

830.88 

725.84 

644.42 

579.47 

55 

6250.5* 

298948 

'96464 

/463J6 

1165.70 

969.81 

823.88 

724.31 

643.22 

57843 

56 

6138.90 

2963.72 

/  953  48 

/456.96 

1161.76 

966.09 

826.89 

722.79 

642.02 

577.5} 

57 

603/.20 

2938.39 

/  942.44 

(450.  8  / 

IIS785 

963.39 

3£4.9/ 

721.28 

640.83 

?76  56 

•$& 

592  7  £2 

29/3.49 

/93/.S3 

(44472 

1153.97 

96070 

7/9.77 

639.64 

57Ji6o 

59 

5826.76 

289901 

/920  75 

143868 

1150.11 

958.02 

82Q97 

7/8-27 

63845 

57^.64 

TABLE  V.— RADII 


57 


DEGREE    OF    CURVE: 

/ 

10° 

n° 

12° 

)3° 

14-° 

IS0 

16° 

1  7° 

/S° 

19° 

0 

57^.69 

52/.67 

479.34 

441.68 

410.28 

333.06 

759.26 

338.27 

5/9.62 

J02.94 

Z. 

577.75 

520./0 

47702 

440.56 

382  22. 

358.52 

337.62. 

3/9.04 

302.42 

4 

569.90 

5/8.54 

4-757' 

439.44 

409  34 

38l'.38 

357  7£ 

336.96 

3/8.45 

301.89 

6 

568.02 

5/6.99 

47440 

43833 

40738 

380.54 

35"  "7  OS' 

336.31 

31787 

30/37 

8 

5/5.44 

473.  10 

43722 

40642 

379.71 

35632 

335166 

317.29 

300.85 

/O 

564  3  1 

5/3.91 

436  12 

40547 

378.95' 

3S5.59 

335:c?/ 

316.71 

300.3.7 

12. 

562  >7 

5/2  38 

470.53 

43502 

404.53 

379.05 

354.86 

33437 

3/6.74 

299.  82 

/4 

5/0.87 

469.25 

433.93 

A03.5? 

37/23 

3S4.I3 

3^3.73 

3/557 

299.30 

16 

55*9*82 

509.36 

46799 

432.84 

402.65 

376.41 

3/5.00 

2.98.  79 

J8 

557  02 

50786 

466.72 

43/.76 

401.71 

375T60 

3*2.70 

332.45" 

3/443 

29£  28 

20 

555!23 

506.30 

465.46 

430.69 

44078 

37479 

351.98 

33/.F2 

313  86 

29777 

22 

553.45 

504.90 

464.2  1 

429.62 

399  86 

373.98 

351.27 

33  IJ  8 

31?  29 

197.26 

24 

551.68 

462.97 

-4Z0.56 

398!  94 

373.17 

350.56 

33055 

312.  7* 

296.75 

26 

549.92 

50/96 

427.50 

398.02 

372.37 

349.85 

32^.93 

312.17 

296.25 

28 

548.  '  7 

50O.5/ 

46Q5O 

426.44 

397.77 

371.57 

349/5 

329.30 

31  1.61 

295  75 

30 
32 

546.44 

499.06 
49762 

459.28 
458.06 

425.4HO 
424.35 

J96.20 
395:30 

370.78 
369.99 

34845 
34775- 

111 

310.50 

295.25 
29475 

54- 

54  3.00 

496.  /  9 

423.32 

394.40 

369.20 

30995 

29425 

36 

541.30 

494.77 

455.65 

422.28 

33  3.  SO 

346.37 

326  83 

30940 

293.^5 

3? 

539.6/ 

49.3.36 

454.45 

39Z.6/ 

367.64 

34-5.68 

326.  Zl 

JOS!  95 

29?.  26 

40 

*3792 

49/.96 

453-26 

42023 

39/72 

36696 

34^.99 

325.60 

3Off3o 

292.77 

42- 

536.25 

49056 

419.22 

390.84 

366.09 

344.31 

32500 

3O7.76 

2-92.28 

44- 

534.59 

489.17 

45o  89 

418.20 

389.96 

343.6Z 

32439 

307.22 

48 

532.94 
S3  /.  30 

48779 
486.42 

449.72 
44-R56 

417/9 
416.13 

388.  Zl 

-364.55 
363.78 

342.95- 
34-227 

323.79 
32  3.  /9 

306.68 
30614 

297/30 
290.  #2 

50 
52 
J4 
56 

529.67 
528.0? 
526.44 
524.04 

425.05 
483.69 
482.34 

447.40 
446.24 
445.09 
44J.95 

4/5.79 
414.26 
4/3  21 
41223 

387.34 
386.48 
385.6-2. 
384.77 

363.02 
.762.26 

360.76 

341.60 
340.93 
340.26 
33960 

32259 
32  /.  99 
321.39 
320.80 

305.60 
30506 
304.53 
30  A.  00 

290.33 
289.85 
289.  37 

5{? 

523.25 

479.67 

44  2..  81 

4I/.25 

383.91 

J6O.O' 

320.21 

3O147 

228  41 

DEGREE 

MINUTE'S 

DEGKfE 

CURVE 

0' 

i<x 

20' 

30' 

40' 

SO' 

CURVE 

2O° 

28794 

285.58 

283.27 

280.99 

278.75 

276.54 

2OO 

21 

274.37 

272.23 

270./3 

268.06 

266.02 

264-02 

2/ 

22 

26204 

260.10 

2S8/8 

256.29 

254.43 

25260 

22 

23 

Z50.-79 

249  01 

24726 

24-J.53 

243.82 

242.14 

Z3 

24 

240.49 

23724 

235.65 

234.08 

^3254 

24 

c 

25 

23/.0/ 

229.5' 

228.02 

226.55 

225.11 

22368 

25 

26 

2Z2.27 

220.88 

2/9.5-' 

2I8./5 

2)6.91 

2/5.49 

26 

27 

2/4.18 

.  2/2.89 

Z//.62 

2/0.36 

209.  /  2 

20789 

27 

28 

206.68 

205.45 

204.30 

203.  '3 

20/.97 

20083 

2g 

29 

199.70 

'98-  58 

19748 

795.3  f 

194.24 

•29 

3o 

\93.f9 

192.14 

191.11 

/  90.09 

189.08 

/  8  8.09 

Jo 

3  / 

187/0 

186.12 

185.16 

JQA  2.0 

183.26 

78232 

3  / 

32 

'81.40 

180.4-8 

179.58 

775.68 

177.79 

176.92 

32 

33 

/  76.05 

175.19 

174.34 

173.43 

X72.66 

I7/.83 

33 

34 

/7/.02 

170.21 

/69.4O 

168.6} 

X67-&2 

167.05 

34 

35 

766.28 

165.51 

764.76 

/640I 

163.27 

/6253 

35" 

36 

/6/.80 

'60.37 

159.66 

I58.9(, 

158.27 

36 

37 

/575F 

156  90 

156.22 

155.55 

154.89 

/  54.23 

37 

38 

IS3.58 

/52'.93 

151.29 

15-1.03 

38 

39 

14-9.79 

143.17 

148.57 

I4.J.97 

147.37 

74-678 

39 

4o 

'4-6.  19 

145.61 

145.03 

144.46 

143.89 

743.33 

40 

4fJ 

142.77 

/4-2  22 

I4/.67 

141.13 

740.59 

I4O.O5 

4| 

. 

42 

'39-52 

13$  99 

'38.47 

137.95 

'3744 

736.93 

42 

43 

736.43 

'35.92 

73543 

'34.93 

/34.44 

'33.9C, 

43 

44 

'33.47 

132.99 

/32.05 

>3I  58 

131.12. 

44 

45 

'30.66 

130.20 

129.75 

12930 

'£885 

1  2g.4l 

45 

46 

X2797 

127.53 

127.09 

726.66 

'2624 

46 

47 

t2S.  39 

/24.97 

/24.56 

'24.  '5 

123.74 

/23  33 

47 

41 

'22.93 
'20.57 

122.53 
120.19 

122.13 

I2/.74* 
119.43 

/2I.35 
"9.05 

/20.96 
7/g-6g 

48 
49 

58 


TA15LE  VI.— NATURAL  SINES   AND   COSINES 


SINB5 


DEGRFE5 

MINUTES 

0' 

10' 

20' 

^ 

4-0' 

50' 

60' 

O° 
/ 
2 
3 
4 

.0000000 
0/74-524 
034.8995" 
0523360 
06975S5 

0029089 
0203608 
0378065 
0552406 
07^6580 

.OO58  1  77 
.O232690 
040//3I 
058/448 
.07555B9 

OO87265 
0261769 
0436/94 
06/0485 
075-4591 

O/I6353 
O290847 
0465253 
06395/7 
05/3587 

0  14  543  9 
0319922 
O49A-308 
0668544 
0542576" 

0/74-524 
0348995 
0523360 
069756F 
OB7I5S7 

89° 
88 
87 
86 
85 

5 
6 

7 
8 
9 

087/53"7 
/04528S 
12/8693 
J39/73/ 

0900532 
1  074-110 

1  24-75-6  o 

/42053/ 
1593069 

.05294-99 
.1103(26 
.12.764-16 
.144-9319 
J62/779 

0955458 
//3203E 
.1305262 
1478094 
.1650476 

0987408 
//60929 
/334096 
1506  £57 
1679/5-9 

IOJ635I 
//898I6 
/3629/9 
/535607 
1707829 

/04S285 
/2<8693 
1391  731 
/56"4-345 
/7J6482 

84 
83 
£2 

a/ 

80 

10 

II 

12. 
13 
14 

.17364-82 
.1308090 
2079/17 
.2JL495// 
24/9219 

I765-/2/ 
/936636 
2/07561 
.2177844 
244-7433 

.1793746 
.1965/66 
.2135988 
.2306/59 
.2475627 

(822355 
1993679 
.2164-396 
.23344-54 
.2503800 

/850949 
E022I76 
ZJ92786 
2362729 
2531952 

1879528 
2050655 
222M58 
2  3  90984 
256008Z 

/908090 
2079/17 
22495/1 
24192/9 
2588190 

79 
70 
77 
76 
7f 

15 

/6 

:i 

/9 

2  5*88  190 
2756374- 

29237/7 

3090/70 
3255682 

Z6I6277 
27^43  a4- 
Z95I5E2 
•3II70£Z 
.3283172 

.Z644-34-2 
.Z8I225I 
.2979303 
.3J4-544-8 
.33/0634 

2672384 
2840153 
.3007058 
.3173047 
.3338069 

27004-03 
£668032 
3034788 
32006/9 
.3365475 

2728400 
2895887 
3062492 
3228/64- 
3392852 

2756374 
Z9237/7 
309O/7O 
3255682 
3420201 

74- 
73 
72 
71 
70 

20 
XI 

zz 

23 
24 

.342020  / 
3583679 
'.3746066 
.39073  // 
.4067366 

544752J 
36I082/ 
3773021 
3934071 
4093923 

.34-74812 
.3637932 
.3799944 
.3960798 
4-120445 

3502074 
3665012 
3826834 
.3987491 
.4I4.693E 

3529306 
3692061 
3853693 
.<*OJ4-I50 
4-173385 

3556508 
37/9079 
388O5/8 
4O4O775 
41  99  80  / 

3583679 
3746066 
39073// 
4067366 
4226183 

fl 

67 
66 
65 

a? 
ae 

2.7 
28 
29 

4-226  133 
'.43B37// 
^•539905~ 
4694-7/6 
4848096 

4252528 
.44^9538 
456J804 
A720380 
'.4S735-/7 

4279838 
44-35927 
459/665 
.4746004 
.4898897 

4305/  /  / 
'44-61978 
4417486 
.477/588 
.4924236 

433  /J48 
4487992 
4643269 
479  7/3/ 
4949532 

4357548 
4513967 
46690/Z 
4g22634 
4974787 

43837// 
4539905 
.46947/6 
.4848096 
5OOOOOO 

64 
63 
62 
61 

60 

30 
3/ 
3Z 
33 

34 

.ffoooooo 

.5/5038/ 
.5299/93 
.5446390 
.55-9/929 

.502SI7O 
.5/75293 
.5323839 
.5470763 
.56/602  / 

.5050298 
52OO/&I 
5348440 
.5495090 
.5640066 

5075384 
'S2249S6 
5372996 
55/937O 
5664062 

5/00426 
5249766 
53975-07 
5543603 
.5688011 

5/25425 
52745O2 
54ai97/ 
.5567790 
S7//9/2 

5(50381 
5299193 
.5446390 
559/929 
.57J5764 

59 

?7 
56 
5-5 

35 
36 

37 
98 
39 

.57J5764- 
.5P7755-3 
6O/8/5"C> 
.'6/566/5" 
.62932O4 

.5759568 
590/36/ 
.604/356 
.(>l79sr/i 
.61/5784 

.57^3323 
,59248/9 
.606  4-5  // 
.6202355 
.63383/0 

5*907^30 

5948228 
.60876/4- 
6225/46 
.6360782 

.5S30687 
597/586 
.6//O666 
.6247885 
.638320  / 

5954294 
'.5994893 
6133666 
'.62.70571 
.6405566 

.5877553 
.60/8/50 
.6/566/5 
.6293204 
.6427876 

54 
53 
52 
5/ 
>5O 

4-0 

41 

42 
A3 

44 

6427876 
!6560590 
669/Jo6 
.(,819980- 
.694-6584 

.64501  3  Z 
.65825/6 
.67/2895 
.6841229 
.6967479 

.6472334 
.6604386 
.67J44Z7 
.6£624-/6 
.69833/5 

6494480 
.66^6200 
.6755^02 
6883546 
7OO9O93 

.65/6572 
.6647959 
.6777320 
.69046/7 
702981  1 

6538609 
666966/ 
.67^8681 
.6925630 
.705"C>469 

656O5-9O 
.669/306 
.68/9984 
.6946584 
-707/068 

49 
48 
4-7 

8 

60' 

5(9' 

40' 

50' 

20' 

10' 

O' 

DEGREES 

MINUTES 

COSINE5 


TABLE  VI.— NATURAL  SINES   AND   COSINES 


S/ME5 


MINUTES 

DEGREES 

0" 

10' 

20' 

3</ 

40' 

50' 

60' 

AS* 

.707/068 

.7O9/  607 

.7112086 

7/52504 

.7/5296-3 

7  173  161 

.7193398 

44° 

46 

.7/93398 

.72/3574- 

.7233690 

.7253744 

.7275756 

.7295668 

.73/3537 

43 

47 

.73/35-J7 

7533345 

.7355090 

.7372775 

.7392394 

.74//95J 

743/448 

4-2 

48 

.743/448 

.7450881 

.74  7025  / 

.7489557 

.7508800 

.7527980 

.7547096 

41 

49 

.75-47096 

.7566/48 

.7585/36 

.7604060 

.762Z9/9 

76417/4 

.7660444 

40 

50 

.7660444 

.7679/10 

.76977/0 

.77/6246 

.77347/6 

.775-3  /2/ 

777/4-60 

39 

$•1 

.777/460 

.7709733 

7807940 

7826082. 

.7844157 

.7862/65 

7880/08 

38 

52 

.7980/08  1.799799  3 

79/5792 

7933533 

.795/208 

.79688  '5 

.7986355 

37 

53 

.7986355   8003  8Z7 

802/232 

8038569 

.8055837 

.8073038 

.8090/70 

36 

54 

.8090/701.8/07254 

£/  24-229 

£/4;  155 

.8/580/3 

.8I7480J 

8/9/520 

35 

55 

.819/520  .8208/70 

82Z475/ 

824/262 

8257703 

.8274074 

8290376 

34 

56 

8230376   .8306607 

8322768 

8339958 

.8354878 

.8370827 

8386706 

33 

57 

.9386706  .84025/3 

84/8249 

84339/4 

S449508 

.8465030 

8480481 

32 

58 

.84804-81  .8495-860 

.85/M67 

8526402 

854/564 

.8556655 

857/673 

31 

55 

.857/675  .85866/9 

860/49  / 

8616292 

.863/0/9 

.8645673 

8660254 

30 

60 

.8660254 

.8674762 

8689/96 

970355? 

97/7844 

.87*2058 

8746/97 

29 

61 

8746/97 

.§760263 

8774254 

3788/r/ 

.8802O/4 

.8815782 

882947* 

29 

62 

.8829476 

.8843095 

8856639 

8870/08 

£8835-03 

.8896822 

89/0065 

27 

63 

.89/0065 

.8923234 

8936326 

8949344 

8962285 

S975/5/ 

8987940 

26 

64 

8987940 

.9000654 

90/3292 

9025853 

.9038338 

.9050746 

.9063078 

^5 

65 

906307S 

907S333 

B087SH 

9095613 

.9  III  637 

.912358-4 

9  |  35455 

24 

66 

9/35455 

.9  147247 

9158963 

9/7O6OI 

,9^2I6| 

.9/93644 

9205049 

25 

67 

92O5-04-9 

9216375 

9227624- 

9238795 

.9249888 

926090Z 

.927/839 

22 

68 

.927/839 

/J282696 

9293475 

9304-176 

9314797 

.9325340 

.9335904 

21 

69 

9335804- 

.9346/89 

93564-95 

9366722 

.9376869 

.9396958 

.9396926 

20 

70 

9396926 

9406935 

9A166G5 

.94264/5 

.9436085 

9445675 

9455/86 

19 

71 
72 

9455/86 
95/0565 

.94646/6 
95/95/4 

9473966 
952-8382 

9483237 
9537/70 

.9492426 

9545876 

.950/536 
.9554-502 

95/0565 
9563048 

19 

17 

73 

9563048 

957/5/2. 

9579895 

9588/97 

9596418 

.9604558 

96(2617 

16 

74 

96/2617 

.9620594 

.9629490 

9636305 

.9644037 

.965/689 

.965925$ 

IS 

75 

965525S 

9666746 

9674/52 

9£g/47£ 

36887/9 

.969S879 

9702957 

14 

76 

9702957 

.9709953 

97/6867 

9723699 

.9  73044-9 

.9737  V/6 

9743701 

/3 

77 

.9  743  70  / 

97-5*0203 

9756623 

9762960 

97692/5 

.9775387 

978/476 

/Z 

78 

978/476 

9787483 

9793406 

9799247 

.9805005 

.98/O68O 

.98/6272 

// 

79 

98/6272 

.98Z/78/ 

9827206 

9832549 

.9837808 

.9842985 

984807# 

/O 

BO 

9848079 

.9853087 

99580/3 

986E856 

98676/5 

9872291 

9876883 

9 

81 

.9876883 

9881392 

95858/7 

9890AT9 

98944/6 

9899590 

.9902681 

0 

82 
83 

990268  / 
9925462 

9906687 
>  92^896  5 

99/06/0 
9932384 

99/4449 
99357/9 

99/8204 
9938969 

.992/874 
9942'36 

.9  92  546Z 
.99452/9 

7 
6 

94 

.99452/9 

.9948£I7 

995//32 

9953962 

.9956708 

.9959370 

.996/947 

S 

85 

996/947 

9964440 

9966849 

9969  f  75 

997/4-13 

.9973569 

.9975641 

4 

86 

'99T564/ 

9977627 

9979530 

999/348 

$983082 

.9  9  8473  / 

.9986295 

3 

87 

9986295 

998777J- 

9989/77 

9990482 

.9991709 

.9992£5-/ 

.9993908 

2 

88 

9993908 

9  99488  / 

9995770 

9996573 

9997292 

.9997927 

9998477 

I 

89 

9998477 

;9995942 

9999323 

99996/9 

.999983  / 

.9999958 

/.oooooo 

O 

GO' 

50' 

40' 

?0' 

20' 

/0' 

0' 

DEGREES 

MINUTES 

COSINE'S 


r,o 


TABLE    VII.— NATURAL   TANGENTS   AND    COTANGENTS 


TANGE-NTS 


MINUTES 

DEGffEPS 

O' 

10' 

20' 

30' 

40' 

50' 

60' 

0° 

.0000000 

.O029O89 

.0058178 

0O  872  6  9 

.OM636I 

.0  14-5454 

.0/7455/ 

89° 

.0/7455/ 

.020365O 

.0232753 

.0261  855> 

O29097O 

.0320086 

O  349208 

88 

2 

.03492O8 

0378335 

.0407469 

.0436609 

0465757 

.04949/3 

052407? 

87 

3 

.0524070 

0553  2  5/ 

.0582434 

.0611626 

.0640829 

067004-3 

86 

4 

.0659268 

.0728505 

.0757753" 

.O7S7OI7 

.0816293 

.0845583 

0874887 

85 

5 

.0874-887 

.09O42O6 

.09J3540 

.09628  90 

.0952257 

.IO2/G4I 

./05/O42 

84 

6 

;|O5VO42 

.1090462 

.1109899 

./)  39356 

.1/68832 

.1/98329 

(227846 

83 

7 

.1227546 

.1286943 

.13/6525 

J346/29 

.  (375-757 

/  405408 

82 

8 

.1405408 

\  1435084. 

.  1464-784 

.14945/0 

.(52  4262 

.1554040 

.1585844 

8/ 

9 

.1583844 

.16/3677 

.164-3537 

.I67J4-Z6 

.1733292 

.1763270 

80 

to 

.1763270 

.\793279 

./823J/9 

.1853390 

./  883495 

.1913632 

J943803 

79 

II 

.1943803 

.1974008 

.2004248 

2034-523 

2064834 

.2095/81 

.2125566 

73 

/Z 

.2125566 

.Z  155988 

.Z/  8644  8 

22/6947 

.2247485 

.2278063 

.2308682 

77 

/3 

.7.308682 

.Z33934Z 

.2370044 

2400728 

.243/575- 

.2462405 

2493280 

76 

14 

.2493280 

.1  524200 

.2555/65 

.25-86/76 

.26/7234 

.2648339 

.2679492 

75 

15 

.2679492 

.•27/O694 

.274/945 

.2773245 

.2804597 

2835999 

2867454 

74 

f  6 

.•28674-54 

2898961 

.293052  1 

.2962/35 

2.9938O3 

3025527 

3057307 

1* 

17 

.30573(77 

.3089/43 

.3/2/036 

.3/52988 

3  /  84998 

.3217067 

3249/97 

72 

/8 

.3249/97 

.328/387 

33/3639 

.3345353 

3378330 

34-I077/ 

3443276 

71 

/9 

.3443276 

.3475846 

3508483 

354//S6 

3573956 

|3  606795 

3639702 

70 

2o 

.3639702 

367-2680 

3705728 

37J884-7 

.3772038 

3805302 

3838640 

69 

a 

.3838640 

'.3872053 

3  90554  / 

.3939/05 

3972746 

'4006465 

4O40262 

€>8 

22 

.404O262. 

.4074/39 

4/08097 

.4/42136 

/f/76257 

'.42/0460 

4244748 

67 

23 

.424474-8 

4279  121 

.43/3579 

4348/24 

4382756 

.4417477 

4452287 

66 

24 

.4452287 

4427/87 

.4522/79 

.4557263 

4592439 

.46277/0 

'.4663077 

65 

25 

4£6?077 

4698539 

4734098 

4769755 

480F.T/2 

.4941368 

.4877326 

64 

26 

.4877J26 

.49/3386 

4949549 

49858/6 

5022/89 

.5058668 

5095254- 

63 

27 
28 

.5095254 
.53/7094 

.5/3/950 
5354465 

'5"I68755 
539/952 

.52  056  7  / 
.5429557 

5242698 
546728  1 

5279839 
.5505/25 

5?  /  709  4 
.554309  / 

62 

61 

29 

.554309  / 

55g//79 

56/9391 

.5657728 

5696/91 

.5734783 

.5773503 

60 

3a 

.577350? 

.58/2353 

585/335 

5890450 

5929699 

5969084 

60086O6 

59 

.6008606 

6048266 

.6088067 

.6/2go08 

.6168092 

.6208320 

6248694 

58 

32. 

.6248694 

.62892/4 

6329883 

6370703 

.6452797 

.6494076 

57 

33 

.6494076 

.6577/03 

.66/8856 

'.6660769 

.670284-5" 

.6745085 

56 

34 

.6745085 

'.6787492 

6830066 

G8728/O 

.69/5725 

.6958813 

.7002075 

55 

JS 

.7OO2  O75 

.70455/5 

7089/33 

.7/32931 

.7/769  // 

.722/075 

.7265425 

5-4 

36 

.7265425 

.7309963 

735469  1 

73996  If 

7444724 

.7490033 

.753554  / 

53 

37 

.7581248 

7627/57 

7673270 

77/9589 

77661  18 

7g/2856 

52 

[78/2856 

.7859808 

.790697-5 

.7954359 

800/S63 

.8049790 

.8097840 

51 

39 

.8097840 

.8/46M8 

8/94625 

.8243364 

8292337 

.834/547 

.8390996 

50 

4o 
41 
4Z 

.8390996 

.9692867 
.9004040 

.8440688? 
8744067 
.90S"6  85  / 

8490624 
8795528 
9/09540 

8540807 
8847253 
9/673/2 

859/240 
8899244 
.92/6965 

.864/926 
895/506 
.92709/4 

.8692867 
9O04-040 
".9^25/51 

49 
48 

47 

4-3 

.932515/ 

9379683 

94345/3 

.9489646 

.9545083 

.960082.9 

.9656888 

46 

44 

•  96  56JJS  SL 

97/3262 

9769956 

982697J 

98843/6 

.9941991 

/.OOOOOO 

45 

GO' 

JO' 

40' 

30' 

ao' 

10' 

0' 

DFGREFS 

I 

MINUTES 

COTANGENT5 


TABLE  VIII.— FROGS  AND  SWITCHES 


61 


FROG 
NO. 

FROG 
ANGLE 

TURNOUT    CURVE 

Theoretic.1 
Lead  AB 

CHORD 
AC 

FROG 
NO. 

RADIUS 

DEGREE 

4 

l4°-/5' 

I5O.67 

^0-46' 

37.67 

37.38 

4 

4% 

(2-4f 

190.69 

30-24 

42.37 

4Z.IZ 

4^ 

s 

I/-25 

2354-2 

24-  3  / 

4-7.08 

46.85 

57 

5k 

/0-23 

284.85 

20-13 

51.79 

5/.58 

1* 

c 

9-32 

339.00 

16-58 

56.50 

J6.3/ 

6 

« 

8-4* 

39785 

/4--Z6 

61.  Zl 

6/.03 

6>2 

7 

8-/O 

46/.4Z 

IZ.-27 

65.92 

65".  75" 

7, 

Tfc 

7-38 

529.69 

10-50 

70-62 

70.47 

7<L 

8 

7-09 

602.67 

9-31 

7S.33 

7£./9 

0, 

8^ 

6-44 

650  35- 

8-26 

80.04- 

79.90 

84 

9 

6-22 

762".75 

7-?/ 

84.75 

84.62 

9 

9| 

6~-OZ 

849.85 

6-45" 

89.46 

89.74 

9^ 

/o2 

5-4-3 

94/.6fe 

6-05 

94.  /  7 

94.0-f 

/O 

II 

5-tZ 

//39.4 

5-02, 

;o3.5"8 

1034-7 

// 

/2 

4-46 

/356.0 

A-I4- 

H3.00 

H2.9O 

/Z 

/3 

4--Z4- 

/59/.4 

3-36 

/22.4-Z 

/E2.33 

/3 

14- 

4-O5" 

/£456 

3-OG 

/3Ag3 

131.75 

14- 

TABLE    IX.-  A-5.C.E.    STANDARD    RAIL  SECTIONS. 


or  HEAD  or  BASE 


L85.  PER  OF   HfAD  OF  B^E 


40 
45 
50 


65- 
70 
75 

II 


27* 


a 


9o 
95 
100 


It 


5%, 


Heigh 
os3 


bose 


TABLE:  x.-  INCMES    »N   DECIMALS    OF  A  FOOT. 


INCHES 


Jfc_ 


.0052 
.0/04 
.0156 
0208 
.0260 
.03/2 
.0365 


O469 
.0521 
.0573 
.0625 
0677 
.0729 
078  f 


.0885 
0937 
0990 


/094 
»/98 


/302 
/354 


.15  IO 
./562 


/667 
/7/9 
177' 
/823 
I97S 
7927 

203  / 


2/35 
.2/87 
.2240 
.2292 
.2344 
.2396 
,2448 


2500 
2552 
2604 
2656 
2708 
276O 
28/2 
2865 


2969 
3021 
3073 
3/25 
3/77 
3229 
3281 


,3333 
.3385 
.34-37 
•34-90 
.3542 

.1146 
.3698 

.3750 
.3502 
.3854 
.3906 


.4010 
.4062 
4//5 


42/9 

4323 
.4375 
.4427 
4479 
'.4531 

4583 
.4635 
.4607 
4740 
.4792 
.4844 
.4896 


.5000 


5/04- 


.5208 
.526O 
.53/2 
.5*65 

54/7 
.5469 
.5521 
.5573 
5625 
.5677 
.5729 


5833 
5895 
5937 
.5990 
6042 
6094 
6/46 
.6/98 


6302 
6354 
6406 
64-58 
65/0 
6562 
66/5 


B 


.6667 
.67/9 

67  71 
!6823 
.6875 
.6927 
.6979 

•7D3I 

.7083 
.7/35 
.7/87 
.7240 
.7292 
.7344 
.7)96 
.7448 


.7500 
.7552 
-7604 
.7656 
.7708 
.7760 
.78)2 
.7965 

.79/7 
.7969 
.8021 
.8073 
.8'25 
.8/77 
.8229 
JSg8j_ 


.8333 
.8385 
.8437 
.84-90 


/O 


.8594 
.8646 


8/50 
8802 
8854 
8906 
8958 
90/0 
9062 
9//5 


INCHES 


9/67 
.92/9 


!9323 
9375 


.9479 
.95  3  / 

9533 
9635 
.9687 

>792 
.9844 
.9896 
92421 


"/* 


0:2 


TRIGONOMETRICAL   FORMULAS 


SOLUTION     OF    RIGHTv  TRIANGLES. 

I.      sin  A  =  %r  ~  cos  B  £.     c.osA  =  4.=  s"'8  -3.   faa  A  -  T~~ 

4. 


•jj=  fe/»5          5.    sec  A  =  £- =  cosecf?      6.  cosecA  =  -| 
-^  =  ^  8.    exsecA=-| 


SOLUT/O/M    OP  OBLIQUE    TRIANGLES. 

sin  A  _   g  sinB  _    fc 

IO'      sin  C  ""  "c"  5/n  C  ~    c 


=  sec B 


12.. 


.4. 


15. 


17.     area  = 


18. 


Let  s 


19. 


GENERAL      FORMULAS. 


2<?. 


'A  4-  COSZA  =  I 

.     ver.5  A  =  /  -  co3A 


S)'n  A 
cos  A 


ton  A 


23.      exsec  A  =   sec  A  —  I 


vers  A 
cos  A 


.MISCELLANEOUS  FORMULAS  AND  THEIR  APPLICATION 


/    Extra   Width  of  Cvage    on    Curves. 

The   auage  should    be    w/dened    ^4"    for    each    c/eyree    of    curve. 

2.  Elevation    of    outer   Roil    on   Curves. 

For    a   speec/   of    55    miles  per  hour  the    elevation  =  ^  X  (degree  of  curve). 
The   e/evof/or?     varies    os    %e    square    of    the    speeo.         Thus    Tor    a     4° 

curve    and    q    speed    of    4-0    miles    per    Aour    elevat/on  =  2.Y 4- Xh^-j  -  4-^. 

3.  Middle   Ordi nates    for    curving    r?o//s. 

Tor   o    3o'  ra'il     the   ordinate.  =  .02  X (degree,  of  curve).      The  ordmate 
vanes  as  the  square    of  the    length    of  roil.       Thus   for  an    8°   curye 

,     »z 
and   a  26'  rail    ord/'nafe  =.O2X8X[|^)  -./2' 


A-.    Pule   for    Keeping    Joints     square    on   a    Curve. 

Cut  a  r<7//   of  any    /en^Hj    eft  a  point  distort?  from    center   of  roil 

hes.  In    1h'i5    formula    L  -  length    of  curve    in   feet 


"yx        inc 


a^c/    D  =•  c/eyree    o/    curve.         L/se.    ^>e    longer    piece      on    the.    outer 
rail     and    Me   shorter     piece,    on     Me     inner     rail. 

5".   Expansion    of  o    S/ee/   Roil. 

Steel    expane/s  .O/     oer   /00'  for   eocA    /J"°/T  r/se    /V?    temperature.. 
Thus     if    #>e    temperature,    changes    from    O°  to  90°   a    30     roil    w/7/ 

ex/W    (o/X^Jf 

G.  To   determine   tne  Decree   of  Curve   of  a  TracK  wiPiouf   a 

First    ^fetfcoc/.        0,o    standard  quaqe   frock    the    degree  of  curve  =  f-p-j, 

in   w/?»cJi    C  =  /OA)^   chord   of  outer  yuo^e   /ne     Tangent    fo    inner 
li'ne,    the    middle,    ore/mate    being  "Hie    gua^e   of     $e    TracK. 

Second  Method.       /f  f/)e    |on^    chord     of  outer   quaqe    line  =  62. 
middle    ordinafe     i'n    inclies  =  degree    of    curve. 


64  MISCELLANEOUS  FORMULAS  AND  THEIR  APPLICATION 


7  Compensation    for  Curvature. 

To    maKe.  resistance  on  a  curve    eooo/  to    resistance  on    o  tanqent 
c/ecrease    1he  grade,    on   ffre    curve     .05"  £  x( degree  of  curve). 

8.  7b/7S   of  Rail  per  Mile    of  TracK. 

The    number  of  tons  of  H240   Its.    in  ,a   m/'/e  of  track-  —xfve'iqhi 

/     * 

per  yard).       Thus    for  a   56  /ts.   ra/7    tons   per  /ft/Ye  =~xS6  =  88, 

9.  Formula     giving     the.    Radius    of   o    Reversed    Curve    fce/Vre«fl 
Parol/el    Taogents. 

Let    p  =perpen<//cu/or    distance    between  tangents, 
and  d  =   length    of    chore/     from    RC.  1o  P.T. 

T/^en    Radius  ~  jl~  .          (exact  formula) 

IO.   Approximate    Vo/ues    of    E,  C    «/?c/  M    for    o   cyrye     Of 
F?ac/ms    r?    and    Degree.    O-        (see  fot/e  It) 
If   A     /s    /ess    %on   2O°, 


IV.      C  -IT^RM  (appro*) 

As   A    /flcreoses      bej/or»c/  2O°    $<?   errc?r  //?     us//?^     Mese   -formulas 
/'/}  creases     more  rapidity       forsnu/os    I    and    III     giving     values 
too    5/2^/7     and     formulas    II    o/ta1    /V       ivin        valves    too 


II.  Correction     for  CurvQ/ore    m    chaining    TracK 

The   correct/on    for  o   /00'  staf/ofl   =.04  X  (degree  of  curve). 

station    should    be.  shortened    hy    ih/s    on>ount  when    c.namtnq    on  inner 

rail   and    lengthened    b«j  "/fee   so/we   amount  when   chawing  on  outer  roil. 


MISCELLANEOUS  FORMULAS  AND  THEIR  APPLICATION  65 


12..    Correct/on    "for    Grode.    in     chaining    TracK. 

In    cboi'ning    on   Q     grocfe    each    loo'  station    should  he    lengthened    by 
an    amount  equal  t>  the  5Q«jor&  of   the    grade    <//v/i/e(/     by    Zoo .        Thus 
on    a    3%    grode.     the    correct/on    per    stof/'oa     /s    —^  =?.O4-S'     and 
•the   correction    per    mile      52.8  x.o4?  =  2.  376  . 

In  it$  genera/  form  1hi$  formula  becomes  ^*~  27>  '  >n  w^/c^  ^  r= 
me  base  of  a  right  triangle  and  h  ihe  altitude-,  h  be//y  small 
in  comparison  w/'w  D  .  A*  -  Me  amount  "the  hupothenvse  is  longer 

than  the.  base.  .  Thus  in  laying  off  a  riqht~- angled  distance,  of 
66'  suppose  an  obstacle  is  encountered  but  a  point"  f»0i/  be  set 
2.l'  off  of  1he  right-angled  lioe  •  The  distance  on  me.  hypolhe- 

Vvse     w/'//    fee    66+^— i.  =  66.04 

/J.   Afc^o</    cf    locating    a   Curve    k>y    Offsets    w/tijot/f    a   TranSn. 
Aoproxim^tc     offset    f  com    tangent"  ~o('j^o)  O»     /^    which   L-  lenqth    of 
ccrve      onof   D  —  dcarcf    of  curvG-  • 

Given    a    a"-3o'  curve .        Station     of    RC,=  /76/32.  ffeauired    to 

set  po/nts     ot     each 


Po.'nf  a  =  PC.  of    corve. 

Extend    ffre    tangent    fro/r    a   to  d     rnakma    aa  =  68 ' 

c</  =  ^(/"S^j  X  ^.5"  =  l.ol  Measuring   68'  frow  a  and    l.ol'  from  d 

/OCO/CS  .  sta^-on    177  of    c. 

Locate    point   h    by   measuring    68   fro/77   c    <?/7</   /.o/'  fro/r?   a  .        he    is 
tangent    to   we   curve,   at   c  .  z 

Extern/   be    t>  e    voting    c.e  =  too'.  ef  =  ^ (;|fjx2.5  =Z.O9 

loo'  from  c    and   2.09'  fro/7?  e     /oco/es  station    178  of  f. 
Extend    chord    cf  to    h     maKinj    fh~'Oo'.  ZX 2.09  =  4.18'- 6g. 

asuring   loo'   from   f    ar»</    4./8'  fro/w   A    locates  station    179  of  q. 

Locate    Hie    remaining     stations    some   os     station  179.       If  "Die   1st. 
is  near  ji>e    P.C  .    set    the    ZnJ   station    from    original    tangent. 


APPENDIX.— FIELD   ENGINEERING  WITHOUT  A  FIELD   BOOK 


Let  & -any  onqle  exyoresse^    in  degrees    one/  decimals  of  a  c/eqree. 
ran  -  natural  tangent  of  A. 
/?-  radius  of  a    curve    wAose   c/eoree  =  D. 
A  may  le.   exyoressec/  in   terms  of    ton    by   $e  tollow/ncj   formulas*. 


fl)     r\~S7.}\Tan-l&>]  for  values  of  tar,  fro, 

f2)     A  '  [60-  ^(ton-^ton  -.6 4  tan         for  WWK   of  ^  from  .25  to.50 

(3)  >U  fc±qfa-jfo-%1f*?    for  valves  of  ton  from. 50  1o.7!> 

(4)  A  =  fa-  ^{ton-^ton  -.O/  for  values  of  to*  from  .75 to  (oo 

For    approximate,    results  t/>e   <7^?/e  formulas    mou  lye  simplified 
•    follows: 

(5)  A  -  S7.3  fen  -for  values  of  tfff  from  O  to.25 
(.6)    A  */60~"g- (fon-. IJjfOn          for  values   of  &/>  fre>/n  .25  to  1.00 

R  way  be  expressed    in    terms  of  D  as   follows: 

ERF?O/?  IN   U5»NG     FORMULAS    5  AND   6. 


Tangent 

HZ 

Angle  by 
Form.  6 

fjroct 
Angle. 

Error  in 
Minutes 

Tangent 

Angle,  by 

BOB  <sy 

Exact 
Anale 

Error  in 
Mi'nu/es 

O.OS 
O.I 
0.2 
0.25 
0.3 
0.4 

2°-5/.9' 
5-43.1 
11-27.6 
1  A-  19.5 

\f-2Z.5 
17-0 
22-0 

2°-S/.S' 
5-42.S> 
II-/2.6 
14-02.2. 
16  -42.0 
2I-40./ 

-fo.i 

+  1.2. 
49.0 
420.3 
4/8.0 
4//.  9 

O.5 
0.6 
0.7 
0.9 
0.9 
l.o 

260-40' 
J/-   0 
JT-  0 
39-40 
4-1-  0 

4-5-  O 

2G-33.3' 
30-578 
34-59.5 
38-39.6 
A  1  -59.2 
45-  O 

+  6.1 
42.2 
40.5- 
4-0.4 
4-0.8 
0.0 

IN    USING  FORMULA  7. 


D 

Radius    bi/ 
Form.   7 

fxoct 

Error 

D 

I    RotHo-i  bf 
Form.  7 

£xocf 
Radius 

Error 

o*-/^' 

229/S.34 

229/^.75 

+.ot 

II" 

521.67 

S2/.  67 

O 

o-?o 

//459.20 

11459.  !9 

+  .01 

IZ 

4-78.34 

4  78  34- 

0 

.0-45 

7639.4-9 

7639.49 

0 

13 

441.69 

44//6S 

4.0  / 

/-    O 

5729.65 

5729.65 

0 

14 

4-/0.28 

•4/O.28 

O 

1-30 

38)9.83 

o 

15 

333.07 

3F^.  06 

4.01 

2 

2g64.94 

2  86  4.  9  J 

4.  Of 

/6 

359.27 

J59.  26 

4.0f 

3 

/9/O.O8 

19/0.08 

o 

17 

330.28 

338.  Z7 

4.0/ 

4 

/432.69 

J432.69 

o 

18 

3/9.62 

3/9.62 

0 

5" 

1  146.2,8 

0 

19 

3O2.94 

302.94 

0 

6 

955.  3  7 

955.37 

o 

20 

29794 

2S7.94- 

O 

7 

8/9.02 

8/9.02 

o 

25 

23A  O/ 

•£31.01 

O 

9 

7/^  70 

7/6.  7# 

o 

30 

193.  /g 

I93./9 

-01 

9 

63728 

4.  Of 

35 

I6f>.  26 

/&€?  2  8 

-.02 

to 

373.69 

573.  €9 

o 

40 

//Z6  .  /6 

146.19 

-.03 

APPENDIX.— FIELD   ENGINEERING   WITHOUT   A   FIELD   BOOK 


67 


EF?f?OR     IN     USING     FORMULAS      I,    Z,   3    AHD   4-. 


Tangent 

Formula  1 

Fxoct 
Ang/e 

Error 

M^'Cfev 

Tory** 

Angle  by 
rormvla  2 

£*"?' 
Angte 

Error 
ggfc 

.005 

O-/72' 

0"-/7.2' 

0.0 

.25 

I4°-OI.S' 

I4°-02.2' 

-0.7 

.Ol 
.02 

0-34.4 
1-08.8 

0-34.4 
1-08.8 

0.0 

o.o 

.26 
.27 

14  -  34.0 
(5-  06.3 

14  -34.5 
15-06.6 

-o.S 

-0.3 

.03 

1-4-3.1 

1-43.1 

0.0 

.28 

/S-3R4 

J5-3B.5 

-O.I 

.04 

2-174 

Z-17.4. 

o.o 

.29 

I6-/0.-3 

I6-/0.3 

o.o 

.05 

2-  51.8 

2-5V.8 

o.o 

.30 

76-420 

16-42.0 

0.0 

.06 

3-  26.G 

3-26.0 

0.0 

.?/ 

/7-  /3.5 

17-  13.4- 

+  O.I 

.07 
.08 

4-  -  00.3 
4-34.5 

4--OO.2, 
4--  34.4 

-fO.f 
+0.1 

i! 

77-44.8 
/8-/S.V 

/  7  -4-4.7 
/8-/S.8 

+  0.1 

+o.\ 

.09 

5-03.6 

5-08.6 

o.o 

.34- 

18  -46.8 

/ff-46.7 

+  0.1 

./O 

5-  42  .7 

5-42.6 

+0.1 

.35 

19-17.5 

I9-/74- 

+  0.1 

.// 

6-/6.7 

6-  /6.6 

+  0.1 

.36 

19-42.0 

/9-479 

+0.1 

./2 

6-50.6 

6-50.6 

0.0 

.37 

2.0-19.3 

20-18.3 

o.o 

.13 

7-  24.  4 

7-24.4 

0.0 

.38 

20-48.4 

20  -48-4- 

o.o 

.14 

7-59.2 

7-5-0.2 

o,.o 

.39 

2/-/8.B 

ZI-/8.3 

0.0 

.AT 
./6 

8-31.8 
9  -  05.4 

f-3/.ff 
-05.4 

o.o 

0.0 

.40 
4' 

g-.'SW 

2/-  48./ 
22-/76 

-o.i 

-O.I 

J7 

9-7*8 

9-38.9 

-O.I 

.42 

22  -46.8 

22-46.9 

-O.f 

J8 

/0-/2.2 

10-12.2. 

0.0 

.43 

23-/5:9 

23-16.1 

-0.2 

.19 

/0-45.4 

IO-4S.S 

-O.I 

.4-4 

23-44.8 

23-45.0 

-0.2 

.20 

1  1  -  /  ff.4 

II-/8.G 

-0.2 

."4-5 

24-73.5 

S4-/3.7 

-0.2 

.21 

II-  51.4 

H~5I.  6 

-0.2 

.4-6 

24  -42.0 

24  -42.1 

-O.I 

.21 

/2-24.2 

/2-24.5 

-0.3 

.47 

25-  f  0.3 

25  -  /0.4- 

-O.I 

.23 

J2-56.8 

12-572 

-0.4 

.4-8 

25-  38.4 

25  -  38.5 

-o.l 

.24 

/3-29.3 

l3-^9.7 

-0.4 

.49 

26  -06.3 

26-06.3 

o.o 

.25 

/4-0/.  6 

14-02.2 

-0.6 

.<5o 

26-J4.0 

26  -  33.9 

+  0.1 

loojenf 

Artf/e  fey 
rormulo  3 

Angle 

Error 

Mtite* 

To^ent 

Aoyle  by 
Formvlo  4 

Exact 
Angle 

Error 
Miftfes 

.50 
.51 

26°-  33.8' 
27-0/./ 

26°-  33.9' 
27-  O/.3 

-O.I 
-0.2 

.75- 
.76 

36*57.9' 
37-  /3.  8 

36°-52.2' 
37-  /4.I 

-0.3 
-0.3 

.52 

27-28.3 

27-28.5 

-0.2 

.77 

37-35.5 

37-3S-.8 

-0.3 

.53 

27-55:3 

27-55.4 

-O.I 

.78 

v?7-^70 

37-57.3 

-0.3 

.54 

28-22.0 

28-22.f 

-o.» 

.79 

38  -IB.  3 

38-/8.S 

-0.2 

.55 
.56 

28-48.5" 
29-/4.S 

2g-49.6 
29-  14.9 

-O.I 

-o.l 

.80 
.91 

•38-39.4 
39-00.3 

33-39.6 

39-00.4 

-0.2 

-o.t 

.57 

29-40.9 

29-4I.O 

-O.t 

.82 

39  -  21.0 

39-21.1 

—O  1 

.58 

30-06.7 

30  -  06  g 

-o.t 

.83 

39-4-1.5 

39-41.  6 

-o.i 

.59 

3O-32.3 

30  -32  '.4 

-O.I 

.84 

4-0-01.8 

40-  01.8 

0.0 

.60 

70-578 

30-57.8' 

o.o 

.85 

40-Z/.9 

40-21.9 

o.o 

.61 

3/-  22.9 

3/  -23.0 

-O.I 

.96 

40-4/8 

40-41.7 

+  0.1 

.62 

3)  -47.9 

3/-479 

o.o 

§7 

•4/-0/.ST 

41  -OI.4 

+  0.1 

.63 

32  -  /2  .7 

5T2  -  /2.7 

o.o 

g 

4-I-2I.O 

41-2.0.9 

f  O.I 

.64 

32-37.2 

32-372 

o.o 

.39 

4-1-40.3 

41-40.1 

w 

.65 

33-01.5" 

33-01.4- 

+0.1 

.90 

4-1-  59.4- 

41-  59.2 

+O.Z 

.66 

33-25.6 

33-25.5 

+  0.1 

.91 

42  -  18.  3 

42  -  /8.  1 

+  O.2 

.67 

33-49.5 

33-49.3 

+0.2 

.92. 

4-2-37.0 

42-368 

+0.2 

.68 

34-/3.I 

34-13.0 

+  0.1 

.93 

42-5-5:5 

42-55:4 

+0.1 

.69 

34  -  36.5 

34-36.3 

+  0.2. 

.94 

43-XJ.g' 

43-13.7 

+0.1 

.70 
.71 

34-59.7 
35-22.7 

34-59.5 
35-22.5 

+O.Z 

+O.2. 

.95 
.96 

4?-3/.9 
43-49.8 

43  -  3/.9 
43-439 

0.0 
-O.I 

.72 

35-45.5" 

35-45.2 

-fO.3 

.97 

44-075" 

44-O7.6 

-O.I 

.73 

36-08.1 

36-07# 

+0.3 

.98 

44-25.0 

•44-25.3 

-0.3 

.74 

36  -  30.4 

36-30.1 

+O.3 

.99 

44-423 

44-42.7 

-0.4 

•7f 

36  -  52.5 

36-522 

+0.3 

1.00 

44-59.4 

4-5-00.0 

-0,6 

IS -52. 
7*~ 


APPENDIX.— FIELD   ENGINEERING   WITHOUT  A   FIELD   BOOK 


l/se   of    Formulas. 

Given     a    4-"  curve.        A  =  37-44'.          Tb    f/>?c/   7T 

2;A  =  /8-5"£.         /5y    /£v<7/    ton  ^_A     is    found    1b   be   between   .3  one/. 4 
5//7C6      //"     &/7  =   .4     !rj     form U/O    (6)      A  =  22°- O' 
o/?</    //^    &/7  —  .7     //?     form  via   (6)      A-    17-0 

Cnonoe  of    .1    in  ian  chanqes  A   by      5-0' 

_  '(.I)  =  .04         .5 +.04-  =.34-  =  Qoproximale.    ton-^  &  * 

lies     between  .25"  and .50  Therefore     use    formula   (2) 

/f   tern  =  .34    in    formula    (a)    4  =  I8.r8°=  l8~-46& 
If  ton  =^35"    //7   formu/a  (z)    A  =/9.29Z  =  /9-/7.f 
of   .01    in     ion    changes  A    hy  0-50.7' 

78-46.8         Jjj(0f)  =.00163  .34  +.00/63  =.34169  -ton-^A.  . 

By   formula  (7)   /f  =  ^2£9.££  +.073(4.) 
T=  f?to/?-L  A   =  /4J2.69  *. 34-169  = 

Exact    for? /8-52=. 34-173,         Error  .OOOO4- 
T  =    489.59,         Error  .Of' 

cW  cos^-A    /77tfy   ^e   </er/Ve</    from   fo/t^A     by 
ye     two     for/7?v/as, 

•3/s?*7fA  +  co5*??A  =  Conz^A 

ana        —  ^7/7^  ^  . 

/4/50     versj-^  =  /  -  cos^£  . 

E— Sr'exsec^-A  .  C.— 2.f?  s//?jrA  .    M-Rvers^-A.     X-/?5;nA.     Y= 

Thus    anu     function     of  a    curve   mau    be     found 
tan  A    or   ~fan-^  A  . 


APPENDIX.—  FIELD    ENGINEERING   WITHOUT   A   FIELD    BOOK 


Tb   find    an    angle     whose    tangent  /s     (greater    ~fhar?     /.OO      f//?c/ 
any/e     corres^ond/na     &    ^    one/    subtract    from  9O°. 

Given     ta/)  -  /246          To    find  A  . 


This     number     //es    between  ,7S    c?/?</   /.OO        Therefore     use    form 
U/G     (4). 

Svbsfituf/nj    tor?  =  .2025682     in    formula  (4-)      gives    3Z°~ 
90°-  (38-44.89  =f/'/S.z'  =  A  . 
Exact  A  =  S/~/f.o',       Frror   o°-o.z 


.To     find     Ihe    tanqent     of     an     angle     (greater     than     45"*     Catfe. 
Ike.     reciprocal      of    1he      tangent     of      {90°-  the    angle.)  . 

ffeauired    ~H?e     tart  ye  /it    of  36°-  4-3  . 
90°~  (tt-43')  =  33°-  '7' 
If  tan    -  .7  /n    -formula  (6)   A=  Zf-o' 
If    ton    -  .£    if?    formo/a  (&)     A  -   ^/-Q 
Change   of      ,1     in    tor?   chorines  A  bj  4°-0 
33'-  17'  2rr 

3.'~  °  -T£r./)=-^  .6f  ot>  =  .66=  appro  x/tfff/e     tan  3?-i7 

2°-/7'  4"  rr 

Tan   3^-17'  //'e5    be.tyYeen.S0    cwc/  .7f       Therefore     use     formda  (3) 
If   to.  ft    =  .66     in    formula   (3)     A  ~  33-25.6' 
If  tan  -  .65     in    formula   (3)     A~  3d-  O/.S 
of    .01     in    tan   changes  A  by     0°-24-.\ 

33*17' 

33^01^  £*-(.oi)  -.0064-3  &5-h0Wto  =.65643  =  tan  33°-i7 


tan  S6°- 43    =  1.52332 ,        Frror  .00007 


OF   THE 

UNIVERSITY 

OF 


THE  LAST  T 


53599 


20410 

.  .••— 

//r  2  /  »  » 

l*^*f    *^X_r 


04109 


